I have always had notifications of new mail regardless of which folder they were filtered into with the exception of junk/spam. That is the standard and default in Thunderbird.

So I think you must have been using an addon extension in order to get a very specific request just on Inbox.

Did you use this : Mailbox Alert 0.30 by Tjebbe Mailbox Alert allows you to specify, for each seperate mail folder, a message, sound and/or a system command that will be executed when new mail is found there. ... Works with Thunderbird 102.0 - 102.*

REgarding getting it to work in more recent version - It looks like the author has decided a complete rewrite is a lot of time and effort and therefore a significant cost to the author which is just not tenable.

I found this: https://github.com/tjeb/Mailbox-Alert/issues/76

Looked around for you and found this addon extension:

• https://addons.thunderbird.net/en-US/thunderbird/addon/filtaquilla/

FiltaQuilla 4.1 by R Kent James, Realraven (Axel Grude)

Adds many new mail filter actions - launch a file, suppress notification, remove star or tag, mark replied or unread, copy as "read", append text to subject.

Works with Thunderbird 112.0 - 128.*

I've not tested it, but it has a 'do not notify' option .

If you use addons please support the author with donations, it takes a lot of time effort and skill to write and importantly maintain programs.

I know this is a bit older (2012) but this setting has been around until recently:

https://askubuntu.com/questions/112622/how-do-i-get-thunderbird-to-give-notifications-for-only-my-inbox

"Show in the messaging menu" > change radio from "For messages in all folders" to "Only for messages in my Inbox folder"

I have not added any add-ons to Thunderbird since the calendar integration started to work without the Lightning add-on.