The above script is (apparently) derived from defective Unity example code that calls .Move() twice per frame.
This will cause you endless difficulty. I suggest you discard this script and instead try this:
I wrote about this before: the Unity example code in the API no longer jumps reliably.
If you call .Move() twice in one single frame, the grounded check may fail.
I reported it to Unity via their docs feedback in October 2020. Apparently it is still broken:
Here is a work-around:
I recommend you also go to that same documentation page and ALSO report that the code is broken.
When you report it, you are welcome to link the above workaround. One day the docs might get fixed.
If you would prefer something more full-featured here is a super-basic starter prototype FPS based on Character Controller (BasicFPCC):
That one has run, walk, jump, slide, crouch… it’s crazy-nutty!!