You can sign into a Trimble account with a Google account, but not the otherway around. Somehow, the old Google accounts turned into Trimble ID’s or ‘All for SketchUp’ accounts.
Before 2019, I would just sign in the Extension Warehouse with all the different google( or TID) accounts I had gathered during the years (one for every company that I had or name change etc.)
With the removal of the sign out option in the 2019 release (because they all want you to log in with one Trimble ID) I thought I would encounter major problems, but ended up with actually not using the extensions, anymore…
(Admittedly, I have a different job, nowadays, so I don’t really need them anymore)
With a classic license, you won’t have to log in, btw, so you can log in any time with another account (until that trial stops…)