I'm a beginner and have a few questions I'd like to ask.

Tinya:

I’m not sure how much I care about privacy,

Well you are here so that’s a first step

Tinya:

The only private email service provider I’m familiar with is ProtonMail

There is also TutaMail https://tuta.com/

I can’t tell you if you should or shouldn’t continue using Gmail vs Switching to something like Proton or Tuta. That comes down to a personal choice, but there are important privacy improvements in those services over Gmail (in my opinion anyway).

As @Expert4870 pointed out regular Proton Mail addresses are not “anonymous” but may still not be accepted due to perceived fraud risks, among other external factors.