If not “faith” then what?

Because I haven't been convinced by something better. That's it.

Note that “faith” doesn’t need to mean some higher power; it just needs to be something you believe without evidence.

According to what definition? Let's look at Merriam Webster, since you're basing your whole argument around their definitions:

1 a : allegiance to duty or a person : LOYALTY lost faith in the company's president b (1) : fidelity to one's promises (2) : sincerity of intentions acted in good faith

2 a (1) : belief and trust in and loyalty to God (2) : belief in the traditional doctrines of a religion b (1) : firm belief in something for which there is no proof clinging to the faith that her missing son would one day return (2) : complete trust

3 : something that is believed especially with strong conviction especially : a system of religious beliefs the Protestant faith

None of these apply to me, or other FOSS advocates I know. I don't have a strong conviction towards my basic axioms, since as I said, I simply haven't come across better ones.

More concretely, the only thing one can prove a priori is “cogito ergo sum” (“I think, therefore I am”). Any further cognitive reasoning requires faith in one or more axioms about the world, e.g. “the world exists independent of my own perception”.

And thus you completely devalue the terms "faith", "religion" etc., because according to you literally everything past "Cogito ergo sum" is faith. Every word you wrote is faith. Everything you think beyond your basic capability to think is faith. It's fine if you want to decide for yourself that this is how you view these words, but it's not how other people use them, because they simply have no utility the way you use them.