I'm not sure which market you're in, but companies here absolutely do reference checks. They will even reach out people you didn't list if they're a shared connection.
My standing recommendation to everyone is to do good work and get better at advocating for yourself to make sure you're either getting the experience or the comp you need to achieve your goals. If you're not getting that, switch jobs. It's much much better to switch jobs every few years if that's what you need to stay motivated than to stay, do the minimum and collect a paycheck.
I can guarantee you that no large tech company takes the time to find shared connections.
On the other hand, why would I have connections who I didn’t make a good impression on? they are useless to me.
I currently work at a 600 person company, I just invited everyone as reference that popped up as a suggestion - I did the same at AWS. Good luck trying to find the people who actually worked with.
My standing recommendation to everyone is to do good work and get better at advocating for yourself to make sure you're either getting the experience or the comp you need to achieve your goals. If you're not getting that, switch jobs. It's much much better to switch jobs every few years if that's what you need to stay motivated than to stay, do the minimum and collect a paycheck.