The time / date in Cinnamon panel does not allow changing from 24-hr to 12 hr a.m / p.m mode. If you go into system setting and change stuff there nothing happens there either. I’ve reboot the system after changing the time format to see if that is having an effect. . . nothing happens. . . . maybe the themes menu has an effect? Maybe not. . . . don’t know. Anyways little bugs persist and show up here and there.
Rich 
That sounds more like a Cinnamon issue. You will likely have to tkae this up with the Cinnamon developers.
Seems currently cinnamon needs to bail out some issues with updated libs/Toolsets
From the Calendar panel app, change the date format to: %F %X, which will display this:
2023-81-21 05:31:00 PM
You can also use %c, which will display like this:
Mon 21 Aug 2023 05:30:17 PM PDT.
This was tested on both Linux Mint and Arch.
I have eos cinnamon on one laptop and yes i can change from 24 hr to 12 hr time in the panel by just toggling use 24 hr clock.
I use Qogir dark Icons and Desktop Cinnamon, applications Arc-Dark, Mouse Qogir.
just checked too and it is generally working… i do not think this is theme related… it changes on panel withnthe slider…
