I am steadily migrating my critical email IDs off Gmail. I'd rather not have Google gather meta-data about my activities.
Now, I'm still self-hosting, but most of my private email is nevertheless being archived and farmed by a company, because almost everyone I talk with is using them. Sigh.
If you want privacy, you need to add a layer of encryption on top.
So no, in that case it's not a whole lot of info.
Own your email domain, but point it somewhere capable.
if you like a no fuzz setup,use fastmail