iMac as a second monitor

There are network solutions like Luna Display that cost a $135.

https://astropad.com/product/lunadisplay/

Then if and when something goes wrong with the old 2010 iMac, you would still need to buy an external display for the MacBook Pro.

Personally I would not bother and just look for a decent external display to use with the macBook Pro.

see > Use an external display with your MacBook Pro - Apple Support

No sorry, the MacBook Pro does not support Target Display Mode.

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

Only the 27" iMacs from 2010 could be used in Target Display mode also, the 2010 21.5" does not support the hardware use as an external display option at all anyway.

If you have a fast local network you could use the free and macOS built-in VNC client:

https://osxdaily.com/2013/04/05/vnc-client-mac-os-x-screen-sharing/

this is not using the iMac as a second monitor, but would allow you to connect to and control the smaller MacBook from the larger screen of the iMac.