OK, I noticed somebody ask this on Reddit, and thought it was worthwhile enough to deserve official FAQ/Errata.
Swim speed: Instead of attempting Athletics checks to Swim, you automatically succeed and move up to your swim Speed instead of the listed distance.
You can also choose to roll an Athletics check to Swim rather than accept an automatic success in hopes of getting a critical success. Your swim Speed grants you a +4 circumstance bonus to Athletics checks to Swim.Armbands: +2 item bonus to Athletics checks. In addition, whenever you use an action to Climb or Swim and you succeed at the Athletics check, add a +5-foot item bonus to the distance you move.
Swim speed's "instead of attempting check" is seemingly the condition to "move up to swim Speed instead of the listed distance".
Armband's +5 speed is phrased to apply when you succeed at Athletics check, so by RAW would the +5' not apply to Swim speed?It's possible to interpret Swim Speed as actually still comprising a succesfull Athletics check despite "instead of" wording.
I guess that gets into whether there is a distinction between "Success" and "Successful check".
It's also possible "and move up to Swim speed distance" isn't meant to be subjugated to "instead of attempting Athletics check".
Regardless, I think a simple change to Armband wording would remove that worry and just read clearer and more concisely:
"whenever you move with a Climb or Swim action, you add a +5-foot item bonus to the distance you move" (34 characters shorter)
Since you don't normally move on a Failed Climb/Swim check, the result is same for that case, yet it works for Swim speed.
Anyhow, it seems the "Instead of attempting check, you automatically succeed and..." phrasing is something that may be used for other rules mechanics, so it seems relevant to recognize the ambiguity from it here, so as to inform how it may be used elsewhere.