I had this exact problem with my first DualSense about a year ago. The left stick started drifting during some intense gaming sessions, and it just kept getting worse. For me, it wasn't worth trying to fix because I'd already had the controller for a couple years and figured the drift would probably come back anyway. Sony ended up replacing it for free under warranty though, which was clutch. Even if you're out of the warranty window, they sometimes do it anyway if you contact support - worth a shot before you spend money.
If you want to try saving it first, the recalibration in settings can help temporarily, but real talk, it usually just buys you a bit of time. I've seen people use compressed air to blow out the stick mechanism, and occasionally that helps if it's just dust. The Nuclear option people mention is replacing the joystick module itself, which runs like $15-20 in parts, but you need to be comfortable with some light soldering or micro repairs. It's doable if you've got steady hands and watch a tutorial, but if that sounds sketchy to you, just replace the controller.
New DualSense controllers are running around $70-75 depending on sales, which sucks when the old one's still kinda functional. But for Elden Ring specifically, you need precise controls or you're gonna get frustrated fast. If you're planning to keep playing for the next year or two, just bite the bullet and get a replacement. The newer batches seem better about the drift issue than the launch controllers were, so you might get more life out of it this time.