Yes, someone in customs at an airport can be treated as functionally “at the border” with reduced protections.
But you are conflating seeking entry with being present inside the country. That’s the legal line, and the Supreme Court has stated it clearly. “once an alien enters the country, the legal circumstance changes, for the Due Process Clause applies to all ‘persons’ within the United States, including aliens, whether their presence here is lawful, unlawful, temporary, or permanent.” [0]
As for the First Amendment specifically the Supreme court has reversed the deportation order of an Australian labor activist due to alleged Communist Party affiliation, concluding that “freedom of speech and of the press is accorded aliens residing in this country” [1]
The Geneva detail doesn’t apply. He was on US soil as a lawful visa holder when he attended the protest. It’s a question of where he was when the government action targeted his protected expression not where he was when Google emailed him.
His departure doesn’t retroactively strip the constitutional protections that applied when the conduct occurred.
[0] https://law.onecle.com/ussc/533/533us693.html
[1] Bridges v. Wixon https://firstamendment.mtsu.edu/article/aliens/