Thanks for screen-clips.
it is set up for a weekly backup.
Change it! The drop-down menu will give you the options. I personally prefer the "every time Lr exits" as you do get a choice to "Skip the backup" if little work has been done.

"...the latest backup is 8th Jan although I have exited LR today so should be todays backup, yes?
You should see at least a 'weekly' one, I would think.
BUT-More Importantly! You should NOT be backing up the catalogs to the same drive/folder location as your Master Catalog. If the drive fails you have lost everything. Catalog backups MUST go to a separate physical drive!
AND- maybe you have been doing this which might explain why you do not see any after 8th Jan.
The choice for Backup location is within the Backup dialog when you close Lr.
I did optimize yesterday - whatever that does!
In general terms- Tidies up the catalog, removing un-necessary data, possibly compacting it. Check it to do so in the Backup dialog.