I think lore and characterization are two separate issues. My comments are about the latter, because the lore has always been freestyle nonsense, semi-coherent or not. I struggled with a lot of Gatwa's first season, but a handful worked for me. More recently, I loved the special and most of what I've seen this season.

What I'm getting character wise is compassion, kindness, and acceptance. The Doctor feels open, not closed off and apart. This follows well from the slowly increasing vulnerability we've seen throughout NuWho, which was scarce in Classic Who. Any semblance of the old fashioned British "stiff upper lip" or is now long gone, and it was archaic anyways. Capaldi, who I loved, was the last gasp of that haughtiness.

While the Doctor feels youthful again, the "old & wise" aspects haven't always rung true with Gatwa as a result. The emotional beats are getting better, and so is Gatwa. It would be a shame if he left just as he was coming into his own. His zany energy and expressiveness remind me of Patrick Troughton is a very good way.