I can't think of a mechanism whereby the email program or browser could be affected by, or even aware of, whether it's wifi or ethernet connecting to the router.

if it thinks there need be no difference - it won't care. Or more pertinently, the programmers didn't think it through/test thoroughly. The permutations are legion. It may very well be in your computer (or the server s/w), be it driver, graphics or PHP, and then the race hazard scenario is a distinct possibility.

I personally would live with it if there is a workaround and it only affects certain usages. Change the driver and you change other things, some noticeable..... And some annoying, then the spaghetti unravels.

FWIW I use a BT (notso) HotSpot and between: the priorities in someone's router, the handover from router to router, the WiFi sharing, the load on neighbourhood pipe (throttling), the CDN, BT's data collection ---- most times I see the effects of lost packets, and failed handshaking.
My F5 button is showing signs of wear.