I think OP is referring to the “Live Preview” for installed (but not active) themes. For Classic themes, this actually loads Customizer (I didn’t know this!) and you can configure all available Customizer settings of the theme being previewed.
But the changes are not saved to the database until you click “Activate and Publish” (an active theme will only show “Publish”).
To OP:
I installed the free version of this Donovan theme shown in your screenshot (your screenshot shows more Customizer options than mine, so that may be the paid version or some of the settings may be coming from a plugin) and below is what I see. Note that this is on WordPress 6.4.1 — so there isn’t anything inherently broken in 6.4.1, whatever is broken is broken just on your own website.
If this is happening to all installed (but not active) classic themes, then perhaps this is a plugin conflict of some sort on your own website. Follow the standard procedure of disabling ALL plugins to see if the problem goes away. If it does, then re-enable your plugins, but one at a time, until the problem comes back: then you’ll know the last plugin activated is the culprit.
Of course, your best long-term course of action is what was suggested by @threadi already: to consider migrating to a modern FSE theme.