I normally use Firefox, but just tried with Chrome (the most-recent version), and do not see what you report.
My Chrome has no extensions installed, especially no ad-blockers and no script-blockers - if you have anything that's not standard Chrome, try disabling them. Also try clearing cache, cookies etc - which on every browser I use I clear all of, every day.
I don't see any feature in FM's preferences that would select everything, however there are two keyboard shortcuts that would do it: asterisk then a, and single-quote then a. Is there any chance that you're typing either of those by accident? If you don't use keyboard shortcuts you can disable them at: Settings - Preferences - Accessibility. You can read about shortcuts at:
https://www.fastmail.help/hc/en-us/a...oard-shortcuts