Can I use my 2019 iMac as a monitor for a 2025 Mac mini?

That iMac is new enough that you can set it up as an AirPlay Receiver for AirPlay to Mac – and use it as an extra screen. AirPlay is not as good as a hardware video connection to a real monitor. I don't believe it will let you use that iMac's full 5K resolution, and there may be lags and artifacts.

Continuity features and requirements for Apple devices - Apple Support

There is a workaround product called Luna Display (Astropad), but even the vendor site says that it has limitations and is not recommended for high-motion content like video editing and gaming.

Get a decent monitor for the Mac mini, one you would be happy using as your main monitor, whether or not you try one of the above.

Your 2019 20" iMac does not have the Target Display Mode feature:

Use your iMac as a display with target display mode - Apple Support

Sorry, no. Invest in a good dedicated monitor.