The starting questions are:

• (Assuming the 30gb is what's on your PC) How does this size compare with what's on the server?
• What kinds of data do you need to keep, or not keep?
• It grew to 30gb from what size, over what period of time?

I don't want to store anything locally, as soon as I can search and open emails with reasonable speed and not having to wait ages.

I don't remember the previous amounts of data.

I don't know how much is on the server but I assume quite alot.

PS: the email notifications we receive are badly designed. They have a huge button which instead being a REPLY button, it is a MARK IT SOLVED button. I accidentally clicked the button to reply in the forum and didn't want it to be solved.

firefoxor said

I don't want to store anything locally, as soon as I can search and open emails with reasonable speed and not having to wait ages.

So your real problem is slowness, not necessarily that you have 30gb, correct?

That said, I come back to this "What kinds of data do you need to keep, or not keep?", and how much does your server show is being used. You need to visit the account information on your mail provider's website and find out how storage is being used.

You haven't replied so apparently not very important, but in case others are following:

• assuming you have IMAP accounts, not pop...
• disable synchronization for each account at Tools > Settings > Synchronization - the caching a imap messages on your PC
• open the profile folder https://support.mozilla.org/kb/profiles-where-thunderbird-stores-user-data
• shut down thunderbird
• delete all the mail files on your PC in the ImapMail directory
• restart