Unknowingly logged into account inadvertently links all accounts?

I have a google account specifically for school where I have to use it a lot since it’s required and most of my schoolwork is done there and a separate calendar app that my teacher required to download on to my laptop along with Microsoft office. Now this is where I have a question. I forgot to log off from both my google account and the apps and exit out of the browser and app, and then I would proceed with logging into my other compartmentalized accounts for hobbies/entertainment on different compartmentalized browsers. Another thing is that I recently started using a vpn service and I’m on the free plan and it’s been just ok so far but there’s been a number of instances where it would switch servers and disconnect, and this is all happening when I forgot to log off my google account and apps while logging into my other hobby/entertainment accounts. I was wondering if I just inherently made it so that my google account and/or all the apps tracked and linked all my hobby/entertainment accounts all together now and also all the ip addresses or am I thinking too much into this? I hope my post makes sense

You can check the logged in IP addresses with your login activity. It’s unlikely to make much of a difference though, in regard to privacy. My suggestion would be to disable search history on your google account, and refrain from using the same browser/(profile) for school as you do for normal stuff.

They are, but IP addresses aren’t enough to identify an individual specifically. On a cellular network, many customers are often behind a single IP address.

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Opsec wise, you don’t want to be switching between compartments manually like that. As you’ve experienced, you’re probably the least secure part of the whole thing.

I’d use separate user accounts for different compartments and block connections without the VPN if possible. That’s if having a VPN actually makes sense. If you didn’t want your account providers knowing your IP, you’ve leaked that info already. If they already knew your IP from before you started using a VPN, it doesn’t do much for that use case.

If your hobby account providers use Google, between that and fingerprinting, Google could probably link all those accounts to you.