It took about a year for me to fully switch. Even now, I haven’t deleted my Gmail address - I just forward everything to my new address at my domain, and whenever anything appears in my Gmail address which I would like to switch over I make it happen.
I even recently did the switch from one mail provider to another while keeping my email address, since I took the advice of people years ago to choose a provider who supports custom domains and use them. Although I spent a fair bit of time researching, the process itself took about 2-3 hours. When people say it’s easy to switch between providers when you own the domain, they mean it.
It’s not an easy task at all, but you don’t have to do it in one hit. Just take your time - in the meantime you hope that your Google account doesn’t get axed, but even if it does you’re in a better position than if you stayed.
On forgetting a random site: use a password manager; then, you have an effective memory of all the services you use as well as their logins. This is something you should do whether you use Gmail or not. (This might be a bit redundant if you use Google to log in everywhere at the moment, but you’ll thank yourself later if you start this now.)