Should the panel in my mobile home be set up as a sub-panel?
You do not need to isolate your neutral and ground if installed prior to 1999 , (I just read something that said 2008 was the date subs had to have the neutral isolated).
In 99 4 wire feeders were required prior to that date 3 wire was legal so if your home is 99 or older the intermixed neutrals and grounds were legal on a sub back then.
Although internet electricians say you can not use water pipes rod pipe and plate electrodes are still in the 2020 code so if someone inadvertently cut your ground it can be reconnected using a crimp splice. Irreversible splices are allowed on the grounding conductor. And water pipes are still legal today current code requires a supplemental method and this can also be a rod pipe or plate electrode but with an older place you may only required 1 and there will normally be 1 at the main panel with a Mobil just splice that wire and you are good again.
Mobile are 50 amp feeders less than 20’ but all the relevant code is located in article 550 of the NEC since you are aware of some code , that section is only about 10 pages long, feeder 550.10,  branch circuits 550.12  grounding 550.16