Tridion uses regular expressions to validate browser versions. The regex for Chrome does not work with versions above 100. You can change this yourself. Just open the file %TRIDION_HOME%\Web\WebUI\WebRoot\Configuration\System.config, look for the line containing '<browser name="Google Chrome 50+"' and change it to:
<browser name="Google Chrome 50+" regExp="Chrome/([5-9]\d+|\d\d\d+)"/>
While you're at it, also change the line for Firefox (because FF is also approaching the 100 fast):
<browser name="Mozilla Firefox 47+" regExp="Firefox/(4[7-9]|[5-9]\d+|\d\d\d+)" />