If the Senate adjourns, doesn’t that mean an immediate recess appointment?
I don’t see how Democrats win here.
No. It's a little complicated. Boils down to SCOTUS ruling that a recess longer than three days is necessary to be a recess long enough to support a recess appointment.
House and Senate run phony pro forma sessions to make sure no recess is longer than three days, on paper only. SCOTUS refuses to see this as a sham, so Congress has usurped the recess appointment power.
The "adjourn/recess" proposal made by Schumer has the typical pro forma sessions in place. It also has a "come back if Pelosi sends us a COVID bill" clause.
Oct 23, 2020 Motion to Adjourn
Mr. SCHUMER. Mr. President, I move to adjourn and to then convene for pro forma sessions only, with no business being conducted, at 12 noon on the following dates, and that following each pro forma session, the Senate adjourn until the next pro forma session: Tuesday, October 27; Friday, October 29; Tuesday, November 3; Friday, November 6. Further, that if there is an agreement on legislation in relation to the COVID pandemic, the Senate convene under the authority of S. Res. 296 of the 108th Congress. Finally, that when the Senate adjourns on Friday, November 6, it next convene at 4:30 p.m., Monday, November 9, and that following the prayer and the pledge, the morning hour be deemed expired, the Journal of proceedings be approved to date, the time for the two leaders be reserved for their use later in the day, and morning business be closed.