not at Adobe, but I've placed enough people there and talked to enough of their in-house team that I can give you a real picture of what the recruiter phone screen looks like. this is not the "preparation tips" fluff, this is what actually happens.
the recruiter screen is 30 minutes, sometimes 45. it's with an in-house TA person, not a hiring manager. the goals: confirm you're actually interested and available get a rough read on level fit (don't waste an onsite on someone who's an L3 for an L5 req) basics of your background screen for obvious red flags
questions you will get in some form: walk me through your current/most recent role and what you're building why Adobe, why now? what's your timeline? any competing offers? where are you in your search? what's your work auth situation? (for US roles) what are your comp expectations? they always ask. have a number ready or a range.
"why Adobe" matters more than people think. "it's a great company" is not an answer. they want something specific: a product you use, a capability you've heard about, a team you know is doing interesting work. if you can't answer this you look disinterested and they'll note it.
what gets people cut at the screen: can't explain what they actually built (vague team-level descriptions) timeline is 2+ months out and they have headcount pressure comp expectations way above band without flexibility signal "I haven't really thought about why Adobe specifically"
speed also matters. if you're responsive between steps they note it positively. if it takes you 4 days to schedule the screen they wonder if you're actually looking.
one thing I'll add: Adobe's TA team is generally professional and communicates reasonably well compared to some companies I work with. you'll usually hear back either way within a week of the screen.