Maybe some cards won't be supported because of their payment network, or because they were issued by non-traditional banks. Paying through Google Pay is the most convenient option for me, and I don't want to give that up.

Personally, I've never had any problems adding a card to Google Pay. But I'm sure there are some restrictions out there, it's just that all my cards have worked without any issues. Check the terms and conditions.

That's right. Some cards are supported, some aren't. You can read about all of that both on Google and in the Google Pay or Apple Pay terms of use. I didn't have any problems adding mine either, even though I use a card from the online bank Roar https://roar.bank.in/en/blog/how-to-add-credit-card-in-google-pay. But again, just because I didn't have any issues doesn't mean that's the case for everyone. You've got the guide, give it a try.