Can't change clock settings on iMac Control centre

Safe Mode is a very safe procedure. Here's how you do and what it does during the initial boot. Beside to follow Note 2 below:

Boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

Restart the iMac and re-visit the clock settings.

If that doesn't help, startup in Safe Mode and a normal restart.

Start up your Mac in safe mode - Apple Support

Restart in Safe Mode, then Restart normally and see if you can turn on Seconds in the Clock Settings.

If a normal restart did not fix the clock switches..?

Safe Mode is really easy.

1. Shut down your Mac.
2. Press and hold the power button on your Mac to turn on your Mac and load startup options. When you see the startup options window, release the power button.
3. Select your startup disk. It's named Macintosh HD, unless you changed its name.
4. Press and hold the Shift key, then click the “Continue in Safe Mode” button below your startup disk. 
5. When you see the login window, you might also see “Safe Boot” in red text in the upper-right corner of the login window. Log in to your Mac. You might be asked to log in again.

Then do a normal restart to get out of Safe Mode.

I've asked the moderators to hide your serial number.

Try toggling some of the other option switches and then turn on the time with seconds switch.

Is the iMac's software up to date? The current version is macOS 15.4 Sequoia.

What's new in the updates for macOS Sequoia - Apple Support

Glad to hear that. You're welcome.