I used to have something similar when signing into youtube to manage one of my accounts using Private Browsing, google would send me emails and text messages saying there was a sign-in on a "new device" (despite it being the same laptop), got annoying to be honest, but one day it just stopped, can't recall if I changed something in the notification settings or their servers just got used to it...
Passwords were rejected in mailwasher outlook etc. and I had to manually login to each account on the google web page where it said something like unrecognised machine blah blah. I had to tick a box to say yes it's me.
Just out of interest this was the email waiting for me when I logged onto the googlemail web page. I nearly hit the panic button before, looking at the ip etc, I realised I was the "someone". Still as I said it was a damn nuisance to login and fiddle with twenty or so accounts. Some I had to go back over as I never initially noticed the "yes this is me" tick box.
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