Show specific comment/post/mention counts on boxes page

[Rahularyan2211]

Currently, we can only see the number of inbox messages through the icon notification badge with the number. However, after going to inboxes, users don't get any info on whether they got a message, post, or comment reply.

This can be fixed by simply implementing the same technique that checks for updates used after clicking the settings button.

[robertnabbe]

Picking this up.

[aeharding]

Blocked until https://github.com/LemmyNet/lemmy/issues/3601