When he chooses Palpatine, he’s making a deal with the devil to “save Padme’s life”, liberating himself from the [Jedi-informed] conscience he did have. It’s not that what he does from here “doesn’t count” but it’s not a reflection of who he is (well, idk, loaded philosophical question) or who he wants to be. Hayden crying is some of the most striking imagery in ROTS and it happens several times.
I think the problem with Anakin’s decision to follow Palpatine is the absurdly extreme cost of doing so that Anakin has to pay right up front. I mean, I can understand Anakin (or anybody, really) agreeing to do some seriously evil stuff in order to save the life of a loved one. But Anakin is told that, in order to save Padme, he has to basically mass-murder everyone he’s ever known, including children. That goes well beyond “my first Dark Side experience”. The justification, I guess, is that Anakin desperately wants to save Padme and he’s slightly pissed off at the Jedi for denying him a Council seat. But this is so weak - the character-work really isn’t there in the script to justify Anakin’s decision. It’s a ridiculous and jarring leap to go from “well I’m now an accessory to Mace Windu’s murder, I might as well just roll with the whole Dark Side thing” to “I will now methodically murder hundreds of people including defenseless children on the off-chance this Sith stuff pans out and saves Padme”.
But I do agree that Hayden crying in silence is one of the few emotionally compelling things that happens in the Prequels.