This problem has been around since 2018 for the intel mini i7 too.. problems started to appear around os 10.14.0.... apple replace my motherboard, (did not solve), and after a few os updates to 10.14.6, external monitors woke up reliably After sleep, short shutdown or even lengthy shudown.
there is a apple forum on this issue with 100s to 1000s of discussions. Every combination of monitor, cable is addressed.... at the end of the day, if a user found something stable and working, that was the best that could be done.
I updated to 11.2.. whamo, same loss of external monitors. I spent 4 hours of frustration switching cables, switching monitors, restarts, hdmi vs usb c, etc., all to no avail. Grrrrrr
I updated yesterday to 11.3. Presto! External monitors work again. But the usb mentor flickers out for a second or so, about once every hour. Random.
clearly, the mini hardware bus has issues... which can be partially addressed by the os. But 11.2 broke what was working well with 11.0 and 10.15. 11.3 makes it better but not 100%.
as soon as iMac m1series come out, I am buying and leaving the i7 mini as a relic.