It'd be surprising if there wasn't a clear or direct causal path about how Google found that information. For example, imagine that you paid for a hotel room somewhere in Thailand by cash, didn't carry your phone with you at the time, didn't log in to any electronic device, and still Google inferred that you stayed there, THAT would be surprising.
On the other hand, literally parsing out an email (AND even linking to it, you can click on the notifs to take you to the relevant email!!!) and showing you the result doesn't in any sense qualify as surprising.
No, but I do think that everyone who gets a service for free should by default assume they don't have much privacy. That is not a huge burden to assume.
I've used a paid email provider since before Gmail existed. They've not been blocked.
I know there are the occasional posts on HN about Gmail blocking their servers, but I doubt it's anywhere close to the norm.
It also sounds like you need to organise your life a bit better. Google's notorious for their screw-ups and service closures, one day you might miss an important payment because they turned off the feature or you end up on the wrong side of an A/B test.