Поддержание положения прокрутки работает только когда не в нижней части сообщения div

window.onload = function(e){ 
  document.querySelector(".messages").scrollTop = 10000;
  
  bottomScroller(document.querySelector(".messages"));
}
  

function bottomScroller(scroller) {
  let scrollBottom = scroller.scrollHeight - scroller.scrollTop - scroller.clientHeight;

  scroller.addEventListener('scroll', () => { 
  scrollBottom = scroller.scrollHeight - scroller.scrollTop - scroller.clientHeight;
  });   

  window.addEventListener('resize', () => { 
  scroller.scrollTop = scroller.scrollHeight - scrollBottom - scroller.clientHeight;

  scrollBottom = scroller.scrollHeight - scroller.scrollTop - scroller.clientHeight;
  });
}

.container {
  width: 400px;
  height: 87vh;
  border: 1px solid #333;
  display: flex;
  flex-direction: column;
}

.messages {
  overflow-y: auto;
  height: 100%;
}

.send-message {
  width: 100%;
  display: flex;
  flex-direction: column;
}

<div class="container">
  <div class="messages">
  <div class="message">hello 1</div>
  <div class="message">hello 2</div>
  <div class="message">hello 3</div>
  <div class="message">hello 4</div>
  <div class="message">hello 5</div>
  <div class="message">hello 6 </div>
  <div class="message">hello 7</div>
  <div class="message">hello 8</div>
  <div class="message">hello 9</div>
  <div class="message">hello 10</div>
  <div class="message">hello 11</div>
  <div class="message">hello 12</div>
  <div class="message">hello 13</div>
  <div class="message">hello 14</div>
  <div class="message">hello 15</div>
  <div class="message">hello 16</div>
  <div class="message">hello 17</div>
  <div class="message">hello 18</div>
  <div class="message">hello 19</div>
  <div class="message">hello 20</div>
  <div class="message">hello 21</div>
  <div class="message">hello 22</div>
  <div class="message">hello 23</div>
  <div class="message">hello 24</div>
  <div class="message">hello 25</div>
  <div class="message">hello 26</div>
  <div class="message">hello 27</div>
  <div class="message">hello 28</div>
  <div class="message">hello 29</div>
  <div class="message">hello 30</div>
  <div class="message">hello 31</div>
  <div class="message">hello 32</div>
  <div class="message">hello 33</div>
  <div class="message">hello 34</div>
  <div class="message">hello 35</div>
  <div class="message">hello 36</div>
  <div class="message">hello 37</div>
  <div class="message">hello 38</div>
  <div class="message">hello 39</div>
  </div>
  <div class="send-message">
	<input />
  </div>
</div>

let scroller = document.querySelector('#scroller');
let anchor = document.querySelector('#anchor');

// https://ajaydsouza.com/42-phrases-a-lexophile-would-love/
let messages = [
  'I wondered why the baseball was getting bigger. Then it hit me.',
  'Police were called to a day care, where a three-year-old was resisting a rest.',
  'Did you hear about the guy whose whole left side was cut off? He’s all right now.',
  'The roundest knight at King Arthur’s round table was Sir Cumference.',
  'To write with a broken pencil is pointless.',
  'When fish are in schools they sometimes take debate.',
  'The short fortune teller who escaped from prison was a small medium at large.',
  'A thief who stole a calendar… got twelve months.',
  'A thief fell and broke his leg in wet cement. He became a hardened criminal.',
  'Thieves who steal corn from a garden could be charged with stalking.',
  'When the smog lifts in Los Angeles , U. C. L. A.',
  'The math professor went crazy with the blackboard. He did a number on it.',
  'The professor discovered that his theory of earthquakes was on shaky ground.',
  'The dead batteries were given out free of charge.',
  'If you take a laptop computer for a run you could jog your memory.',
  'A dentist and a manicurist fought tooth and nail.',
  'A bicycle can’t stand alone; it is two tired.',
  'A will is a dead giveaway.',
  'Time flies like an arrow; fruit flies like a banana.',
  'A backward poet writes inverse.',
  'In a democracy it’s your vote that counts; in feudalism, it’s your Count that votes.',
  'A chicken crossing the road: poultry in motion.',
  'If you don’t pay your exorcist you can get repossessed.',
  'With her marriage she got a new name and a dress.',
  'Show me a piano falling down a mine shaft and I’ll show you A-flat miner.',
  'When a clock is hungry it goes back four seconds.',
  'The guy who fell onto an upholstery machine was fully recovered.',
  'A grenade fell onto a kitchen floor in France and resulted in Linoleum Blownapart.',
  'You are stuck with your debt if you can’t budge it.',
  'Local Area Network in Australia : The LAN down under.',
  'He broke into song because he couldn’t find the key.',
  'A calendar’s days are numbered.',
];

function randomMessage() {
  return messages[(Math.random() * messages.length) | 0];
}

function appendChild() {
  let msg = document.createElement('div');
  msg.className = 'message';
  msg.innerText = randomMessage();
  scroller.insertBefore(msg, anchor);
}
setInterval(appendChild, 1000);

html {
  height: 100%;
  display: flex;
}

body {
  min-height: 100%;
  width: 100%;
  display: flex;
  flex-direction: column;
  padding: 0;
}

#scroller {
  flex: 2;
}

#scroller * {
  overflow-anchor: none;
}

.new-message {
  position: sticky;
  bottom: 0;
  background-color: blue;
  padding: .2rem;
}

#anchor {
  overflow-anchor: auto;
  height: 1px;
}

body {
  background-color: #7FDBFF;
}

.message {
  padding: 0.5em;
  border-radius: 1em;
  margin: 0.5em;
  background-color: white;
}

<div id="scroller">
  <div id="anchor"></div>
</div>

<div class="new-message">
  <input type="text" placeholder="New Message">
</div>

window.onload = function(e) {
  let messages = document.querySelector('.messages')
  messages.scrollTop = messages.scrollHeight - messages.clientHeight
  bottomScroller(messages);
}


function bottomScroller(scroller) {
  let oldScrollTop = scroller.scrollTop
  let oldHeight = scroller.clientHeight

  scroller.addEventListener('scroll', e => {
    console.log(`Scroll detected:
      old scroll top = ${oldScrollTop},
      old height = ${oldHeight},
      new height = ${scroller.clientHeight},
      new scroll top = ${scroller.scrollTop}`)
    if (oldHeight === scroller.clientHeight)
      oldScrollTop = scroller.scrollTop
  });

  window.addEventListener('resize', e => {
    let newScrollTop = oldScrollTop + oldHeight - scroller.clientHeight

    console.log(`Resize detected:
      old scroll top = ${oldScrollTop},
      old height = ${oldHeight},
      new height = ${scroller.clientHeight},
      new scroll top = ${newScrollTop}`)
    scroller.scrollTop = newScrollTop
    oldScrollTop = newScrollTop
    oldHeight = scroller.clientHeight
  });
}

.container {
  width: 400px;
  height: 87vh;
  border: 1px solid #333;
  display: flex;
  flex-direction: column;
}

.messages {
  overflow-y: auto;
  height: 100%;
}

.send-message {
  width: 100%;
  display: flex;
  flex-direction: column;
}

<div class="container">
  <div class="messages">
    <div class="message">hello 1</div>
    <div class="message">hello 2</div>
    <div class="message">hello 3</div>
    <div class="message">hello 4</div>
    <div class="message">hello 5</div>
    <div class="message">hello 6 </div>
    <div class="message">hello 7</div>
    <div class="message">hello 8</div>
    <div class="message">hello 9</div>
    <div class="message">hello 10</div>
    <div class="message">hello 11</div>
    <div class="message">hello 12</div>
    <div class="message">hello 13</div>
    <div class="message">hello 14</div>
    <div class="message">hello 15</div>
    <div class="message">hello 16</div>
    <div class="message">hello 17</div>
    <div class="message">hello 18</div>
    <div class="message">hello 19</div>
    <div class="message">hello 20</div>
    <div class="message">hello 21</div>
    <div class="message">hello 22</div>
    <div class="message">hello 23</div>
    <div class="message">hello 24</div>
    <div class="message">hello 25</div>
    <div class="message">hello 26</div>
    <div class="message">hello 27</div>
    <div class="message">hello 28</div>
    <div class="message">hello 29</div>
    <div class="message">hello 30</div>
    <div class="message">hello 31</div>
    <div class="message">hello 32</div>
    <div class="message">hello 33</div>
    <div class="message">hello 34</div>
    <div class="message">hello 35</div>
    <div class="message">hello 36</div>
    <div class="message">hello 37</div>
    <div class="message">hello 38</div>
    <div class="message">hello 39</div>
  </div>
  <div class="send-message">
    <input />
  </div>
</div>