Screen sharing shuts down at sleep

I've been using a setup with two computers for ages, where I manage the secondary one via screen sharing from the primary one.

This has worked flawlessly until recently, probably after a system upgrade. Now the Screen Sharing app always shuts down when my primary computer goes to sleep, meaning I must start the app and reconnect to my secondary computer every time I wake up my primary one.

A bit tedious. Is this a new security "feature" or is there some kind of setting that I can change to keep Screen Sharing alive and stay connected to my secondary computer?

(I'm on Ventura, not 13.1 as the "smart" device list says …)