This sounds very similar to what I experienced with my 2018 GT2. My handling got progressively 'squirrelly' – felt like the car would randomly fight me to stay in its lane. It wasn't extreme, but definitely unnerving enough that I'd have to white-knuckle the steering wheel when being passed, especially on two-lane roads. My confidence in the car's straight-line stability really dropped.
I took it to a shop about 8-9 months ago. They did an alignment, which helped marginally for a short time, and told me the wheels were 'fine, not bent enough to be concerned about.'
Still feeling unsure, I took it to a different shop just last week. They immediately found and showed me footage – my front-left and rear-right wheels were significantly bent, especially the rear-right one. Whether the issue worsened over time or the first shop missed/downplayed it, I'm not sure.
Anyway, I've pulled the trigger on new rims (switching from the stock GT2 rims/Nitto Motivos to a slightly wider staggered setup), new Michelin Pilot Sport A/S 4 tires, and a full Eibach sway bar kit (front & rear). Everything should be installed before the end of this month (April '25). I'm pretty confident this will resolve the handling issues, and I'll try to remember to post an update here afterward!