Is my Stylus damaged?

Please. Reality check: 2 hours is 2 hours. Cart good for a thousand easy. Not to mention runout is zero signal, much less wear than playing music. So chill.

Over the decades I've left my share of needles dancing around lead out grooves for a couple or three hours.  Two or three times I stupidly let a record spin around all night.  It definitely spun my brain around a bit, but it never physically harmed a thing.

You wore in a deeper runout groove, that’s about it. Next...

I seriously doubt any damage done. 

Fully Manual TT: I tried some inexpensive after-market lifters, no success, then bought this excellent auto-lifter

https://www.amazon.com/gp/product/B07HKX6WL7/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

love it, however, you need room between the edge of the platter and edge of the arm mounting plate. Some TT like my JVC, many Denon's have a wide rim around the platter, reducing available space for placement. Some have enormous arm plates.

It fit between my JVC TT81 Rim and my long arm's small base, but no room for it between my 9" arm's base and platter edge because the shorter arm hole is closer to the platter, reducing available space.

It should be OK.