Yes, we are aware; comment counts do not appear to be updating when viewing the main page.
We apparently have a resource availability issue. As far as I can tell, the counts are being updated correctly. (Yay!)
The problem seems to exist in a layer in which I lack expertise. The assistance of site admins has been requested.
UPDATE 20:23 23-02-2022
The problem has now been resolved. Many thanks to mechanicjay for fixing it again. As of yet we do not know the cause of the local mysql query node failure on one of our servers. However, as some of you have already deduced, there are many background tasks that are managed by the scheduler including updating comment counts, issuing moderation points, updating the journal index on the front page etc. The scheduler couldn't access the database and therefore couldn't do any of the tasks that we expect it to do.
In addition to expressing our gratitude to mechanicjay I would also like to say thanks to all in our community for your patience and good-humour in this rather protracted fix.
It is the slashd daemon. Instead of using a cron daemon to run scripts that do various pieces of site maintenance, they wrote their own replacement. That was not necessarily a problem on its own, but the system it is set up on doesn't have any sort of watchdog or service management. So when it goes under, there is no automatic maintenance or failure notifications if they don't notice the problems on their own.