You should be able to drag Widgets to where you want them while in the Edit Widgets mode.
How to position Widgets
- Secondary click (right click) on the desktop
- Select Edit Widgets
- Add the Widgets you want
- Drag them where you want them
- Click on the Desktop to exit Widget-editing mode
More info from Apple: Add and customize widgets on Mac - Apple Support
When I follow the above steps, I can place Widgets where I want them and they stay there.

Have you rebooted your Mac? If not, that's the first step. If that does not help, then see if the problem is present when you boot in safe mode. That process performs some system cleanup and clears caches, and also disables 3rd party extensions that may cause problems.
Start up your Mac in safe mode - Apple Support
If that does not correct the issue, test in a new user account. A newly-created user account will have all settings at default, and if the issue does not occur in that new account then it provides guidance on what may need to be changed to correct the issue.
Add a user or group on Mac - Apple Support
Once the testing is complete, the new account can easily be deleted.
Delete a user or group on Mac – Apple Support
Those steps will help to isolate the problem.