You can't detect whether a URL handler worked correctly in a browser; otherwise Windows will appear with a "Select an app to open YOURPROTOCOLHERE://" which is completely nonsensical to the user.
As for option 2; ask them every time, or edit their hosts file. Easiest decision in the world: Edit their hosts file, every time, no question. The 1% of nerds who care, and oddly enough don't buy Adobe software, are completely meaningless to the 99% of customers who experience the decision positively.
What a ridiculous conclusion.
Why does Adobe need to exfiltrate some information from my machine anyway? If I'm a customer, then they should know this when I sign into my account. They absolutely don't need this information if I'm visiting their website without logging in.
Modifying a global system file is something their software shouldn't be doing in the first place, but relying on this abuse to track me on their website is on another level of insidious behavior.
If you're worried about device fingerprinting, Adobe has far more reliable ways to do it already. Canvas fingerprinting, IP tracking, cookies. A hosts entry tells them almost nothing they couldn't get elsewhere, provides them with almost no entropy, and attributing insidious intent to what is most plausibly a UX feature is conspiratorial.
I'm not worried about this, since I don't use Adobe products. I'm just calling out what's clearly user hostile behavior. Considering the amount of hostility Adobe has exhibited towards its users over the years, I'm inclined to believe this is yet another example. Nothing conspiratorial about that. If anything, calling this a "UX feature" without any evidence either way is suspiciously dismissive.