I would guess a user with a lack of knowledge, not a bug.

Gmail is special, but starting with basics.

1. Is the account IMAP or POP. I am guessing POP, as IMAP is a synchronised setting, so a deletion in one client will delete it everywhere. Before you can compare apples with apples you would have to satisfy yourself all clients access with the same protocol.

2. Thunderbird has an option to manage what happens with POP accounts when a message is downloaded from the inbox. Tools > account settings > server settings where you can choose to delete the message off the server with several option as to when or to leave message on the server permanently.

3. Gmail account have an override setting on their web site that allows you to tell gmail to ignore all of the clients delete commends and to choose some google specific actions instead. This should take you to the relevant gmail setting page https://mail.google.com/mail/u/0/#settings/fwdandpop

Hi Matt, thank you for your kind reply. I haven't been notified on my e-mail but i see your reply now and cannot check these things right now. Me saying that i tried imap and pop is not enough (do i remember correctly?) and now should try your 2. reply first (i think this i tried too - but again not perfect memory of mine). See you soon.

Okay (Hello again Matt). I have this problem with pop (imap seems ok but i've always prefered pop having all locally even if another client has removed an e-mail earlier) 1. pop: when a mail arrives it is marked/styled with bold text until it is clicked and read. When it changes to not-bold text - means it's been read and then removed from the server. This is the problem i have and might have missed this detail because i probably mostly clicked the new emails immediately after arrival or did something like that not noticing that this is the reason my e-mails are removed from the server.

2. imap regardless of chosen setting about removal only locally (translation of radio button "will be marked as removed" so not removed) i removed mail on the client is removed in the server). E-mails marked as read are still on the server and can be fetched by other e-mail clients which is ofcourse a must-be.

(Edited) Oh. And i still haven't follow-up the instructions from you 3. point of the answer to my post. I tried some not typical gmail settings at that time i wrote about the problem, but must see the 3. point to see if i missed something. Yet the 1. point about pop in this reply here is still relevant i think.

(Edited 2) And my thunderbird version is the latest 68.11.0 i updated it for the need of this reply.