To enable Google Services on Xiaomi MIUI 12, do the following:

Goto Settings -> Apps -> Permissions -> Autostart. Enable both options for ‘Google Services Framework’ i.e. ‘Allow apps to start automatically’ + ‘Allow the app to be started by other apps. Reboot your phone.

Credit: https://amp.reddit.com/r/Xiaomi/comments/i87vl4/updated_my_mi8_to_miui_12_however_i_cant_connect/