Have you sorted Dumbledore before? He seems like a great candidate for this framework, especially with how divisive he is and with how much about him is open to interpretation. I really love your thoughts on this!
I think he's a Snake Bird, like Voldemort.
Albus has a pretty clear Bird secondary. He loves collecting (trinkets, artifacts, interesting memories.) His first step when fighting Voldemort is doing a big research deep-dive into his past. He loves a complex multi-step plan - the chain of events caused by the specific wording in his will is probably the clearest example of that. Voldemort once describes him as "omniscient" and that is the goal - Albus wants all the information, all the time. He also loves his Wacky!Dumbledore persona. It's fun, and it's great for throwing off suspicion. Very Actor Bird of him.
I do think his confrontation with Barty Junior at the end of Book 4 is interesting, because that's the most *pissed* and out-of-control we ever see him. There, the energy is very kick-down-the-door Lion secondary. Burst in with his guys at his back, stun him, physically kick him over, and give Barty Veritaserum so he tells you everything. (And then lose track of him in the aftermath, resulting in him getting Kissed.) I think a Snake secondary could have finessed that a little better. Maybe come at him a little softer, used Legilimency, gotten more info out of him, used him as a hostage... but Dumbledore is a Bird secondary who was missing a MASSIVE piece of information, he needed time to re-calibrate. Bird secondaries who have been very wrong-footed or are put in very unfamiliar situations often start looking like Lions.
In terms of Primary... I think he's a very, VERY Burned Snake who models "For the Greater Good" Bird because it doesn't feel safe to trust people (and 'people' does include himself.) Like he'll talk a good game, but when it comes down to it:
"What did I care if numbers of nameless and faceless people and creatures were slaughtered in the vague future, if in the here and now you [Harry] were alive, and well, and happy?"
The thing with Grindelwald hit him with the intensity of a Snake just really connecting with a Person for the very first time. Because like... young Albus just didn't have any connections like that. Elphias Doge worshiped him - which isn't an equal relationship. Ariana preferred Aberforth, his mother was entirely focused on Ariana, his dad was in prison. And Aberforth... is important, and I think Albus actually really did want and continues to want his "rough, unlettered, infinitely more admirable" brother's approval. But at that point, Aberforth thinks that Albus is a selfish, irresponsible jerk.
But then Grindelwald betrays Albus, which shatters him for a while. Grindelwald's running around Europe, Albus is hiding at Hogwarts because he's too Burnt to do anything else. He fundamentally does not trust himself anymore, he doesn't trust the instincts of his Snake primary. I'm not sure he ever does again, until maybe Harry. Albus thinks he's right about Snape, but he doesn't know, which is why he likes that visual check-in that Snape's Patronus provides. Albus starts modeling Bird primary, hard, because it hurts a lot less to live in that space.
But like he can't cut that Snake primary out of him completely. It's too core to who he is, he'll die. The Drink of Despair (and the Mirror of Erised) takes him right back to his People. He needs these connections, but those connections don't feel safe. Enter Hagrid, clearly very important to Albus - despite being not especially useful and often kind of a liability. But what he IS is someone very Aberforth coded... who will never leave or betray him. (Because Albus has just so much power over him.) I've written about Dumbledore's habit of collecting strays before, but I think it's a Burnt/Exploded Snake thing. He wants connection, but also sees connection as dangerous, so this is his (subconscious) solution.
Generally, when Albus does dumb things, it's for Snake reasons. Putting on the Resurrection Stone? Trying to talk down Draco when he should have just stunned him (and died Master of the Elder Wand?) In that moment Draco is one of his students (who he IS loyal to.) But he's also kind of Aberforth - totally outclassed, shouldn't be here at all, just trying to protect his family.
The house-matching helps explain why Dumbledore and Voldemort just... get under each other's skin to the extent that they do. They have a very emotionally charged relationship, considering that they prefer to keep each other at a distance and only interact through proxies. Albus has a deep distrust of Tom from the word go, even when Tom hasn't actually done much apart from be a creepy ten-year-old. (Tom probably reminded him of Grindelwald ngl. Or himself.) Albus has his collection of Voldemort's most important memories, and Voldemort is uniquely afraid of him. Diary!Tom frames the Basilisk vs Phoenix battle as a conflict between himself and *Dumbledore.* Like these two are wrapped up in each other, and I think it's because they're actually very alike.
