That's a weird ass problem to be honest. The only thing I could possibly think of is maybe you have some really strange QoS settings that severely limit certain traffic types. when you open a browser.
but even then i would assume that to be a router issue more than a pc one.

few suggestions would be running a ping test / tracert to ffxiv servers with and without a browser open maybe there's a dodgy hop somewhere that gets throttled easily...

can you revert windows 10 to previous build and check that. or temporariliy install 7/8 in a dual boot environment / spare hdd. see if the problem persists.

it's a really weird problem honestly