Playback is perfect to begin with, but if I skip ahead to around the 2 hour mark, playback suddenly becomes choppy/laggy. If I go back to the beginning, playback is fine again, so it's not like my computer is being overworked or anything. Also, I have plenty of free space and RAM.
One possibility is you have effects at the 2 hr mark that slow down the timeline. Try making a snapshot duplicate of the timeline, open that, remove all Fx via CMD+A to select and Edit>Remove Effects. Then check playback smoothness at various points on the timeline, esp. the 2 hr mark.
Another possibility is you're using background rendering and it hasn't had a chance to auto-render to cache the 2 hr point. For evaluating things like this it's often best to disable background rendering in FCP preferences, delete all render files via File>Delete Generated Library Files>Delete Render Files>All. That avoids performance variation caused by various timeline regions being rendered vs not rendered.
After removing all Fx from a snapshot of the timeline, if it's still slow, please post the detailed media characteristics. You can do that by using the 3rd-party tool MediaInfo or Invisor. I personally like Invisor because it has a side-by-side comparison mode that allows inspection of multiple clip metadata in an Excel-like grid: apps.apple.com/us/app/invisor-media-file...or/id442947586?mt=12