Swan enjoyed a "full-circle moment" on her return to Wimbledon when she moved past Romania's Irina-Camelia Begu to claim her first Grand Slam main-draw win since defeating the same opponent in 2018.
But the 27-year-old was handed a difficult second-round draw in the form of 2025 Australian Open champion Keys.
Fresh from winning her fourth grass-court title at Eastbourne last week, Keys dropped just one game in the first set - although the opener was much closer than the 6-1 scoreline suggested as Swan squandered four break points.
The Briton, who considered retiring from tennis in 2024 because of a persistent back injury, had better luck in the second set and twice broke back, but Keys' quality prevailed despite having a partisan Court One crowd cheer against her.
Having been ranked as low as 1,114th just 14 months ago, Swan - now the world number 196 - said this year's Wimbledon has been "really positive" for her.
"It's quite surreal to think I was playing on Court One today, and 14 months ago I was playing a 15K in Sharm el-Sheikh. I have come quite a long way," said Swan, who has recently been competing on the lowest rung of the ITF women's circuit.
"It's been gradual and steady. That's kind of the goal from here, is to keep building my ranking week to week and earn my spot at these big tournaments."
Fearnley, meanwhile, fell short in a near three-hour contest against world number 44 Munar, who served superbly throughout.
Munar hit 15 aces, while Fearnley was hindered by eight double faults, and made significantly fewer unforced errors (15) than the Briton (45) in a solid display.
Fearnley managed to create more break point opportunities than Munar, but ultimately only managed to clinch two of those 10 openings as he missed out on a first third-round appearance at Wimbledon.
It briefly looked as though Choinski - the last of the four British players to step on to court on Thursday - might join Fery in the third round when he moved a set up against 17th seed Tiafoe.
But after creating 11 break point chances in the first set, Choinski fashioned just one more across the rest of the match as a re-energised Tiafoe charged ahead.