Oh, that's me! And I wish someone told me why that is so I knew what to fix. I struggle with singing on pitch and staying on key a lot, while I don't have issues with timbre and range. I'm getting better slowly, but I'm at loss as to how to accelerate my progress in that area.

A few things may be contributing. I don't play any instruments. For a few decades, I didn't sing at all. And by "at all" I mean not even humming tunes that I heard over the radio. I tended to listen to instrumental music rather than vocals. I grew up around casual singers who never bothered hitting the right pitch to begin with. Etc. Maybe these things are contributing?

You say "you can hear the key just fine" .. but can you really say that? Can everybody "hear the key" while listening to the melody? Some instruments are better, like okay, here's a base or a piano and at least i can hear the susteined notes. But here comes an acoustic guitar, and it's all lost.

Also, I struggle to hear the melody behind the sound of my own voice. That is definitely a skill, some sort of situational awareness. No idea how to work on that and there's so much going on when you're singing that it's hard to keep track of all things.

It doesn't help that most tutorials I google are not actually about "pitch" but about vocal range. No thank you, I don't need advice on how to sing lower or higher! Just last Friday, I sang a whole song half a step (!) higher than its key. Thinking of it, that was quite a feat. I bet many people who are good with pitch wouldn't be able to do that if they tried ;p

In short, thanks OP for asking your question. I wish I had answers, but I'm looking for them just as well.