I logged into my school-based Microsoft account on my personal laptop. But is it possible that somehow my school is monitoring my Google searches and other browsing history through the school Microsoft account? If my activity is being monitored by my school with the aid of the Microsoft account, does a VPN prevent it from happening?
Logging in to a microsoft portal on a personal laptop that has no remote control software installed does not permit monitoring or control of any other activities outside the realm of the microsoft products being used with or without a VPN in place.
If, however, you have remote control software installed on your computer, whether it's been pushed by microsoft products (e.g. intune), then anything the software is capable of becomes available to the controlling party, regardless of you being on a VPN.