Galvitar is different. It's not gaining Doublestrike or Sweeping during the Damage and Effects step, you're picking which you're using when you make the attack. So, you've been playing Galvitar correctly.
I see what you're saying, but it's kind of weird.
With the Deptonne Berserker, I don't have a choice, so I make an attack. The target gets a Bleed token during the "damage & effects" step, then instantaneously a keyword gets added to his attack, so when he reaches the "additional strikes" step, he makes a second attack... because he still doesn't have a choice (e.g. it's part of his only attack).
With Galvitar, I have 2 choices to make. First, I choose Galvitar's full-action attack. Then, because I have a choice from the beginning, I must choose which keyword that attack has, and I'm locked into that choice throughout the attack (e.g. can't change my mind after the "damage & effects" step).
What if Galvitar's keyword (or a similar attack with choice of "Doublestrike OR Sweeping") depended on a requirement, like the target having a Bleed token? Then I'd have no choice (regular strike) until the "damage & effects" step, then a Bleed gets handed out and suddenly it gains a choice of keywords: either Doublestrike or Sweeping. Since I didn't make the choice during the "declare attack" step, am I out of luck and stuck with a basic single attack? Or since it just got activated, do I get to choose on the spot? This would imply that it's advantageous to have an ability that only becomes active midway through an attack than the same ability that you had the whole time...
Another weird case would be an Enchantment like Debilitate but that turns off/on traits like Doublestrike or Sweeping. If I lost and then gained Doublestrike or Sweeping midway through an attack through revealing and/or removing of Enchantments, then I might be able to gain the choice and switch to a Sweeping vs Doublstrike midway through the attack, compared to having to choose earlier in the attack and sticking with the decision.
As you can see, it gets weird if there's a double standard between abilities that become active "just in time to trigger" vs ones that you had the whole time but had to choose between way back in the "declare attack" step.
(Of course, for creatures and equipment with more than one
different attack, I agree you choose which attack during the "declare attack" step; but Galvitar (and a few others) have an attack with a choice of traits for that attack, which is weird that the choice has to be made during "declare attack" when possible, but the traits (and potentially the choice) might change if the traits have some sort of delayed application.