I am not a vet and not a rehab therapist. My best recommendation would be to check with the rehab place if you can afford professional rehab and if your schedule allows you to take her for rehab. There's so much that is not clear here, and I hope a rehab therapist can see what's really going on. When you say she is keeping her foot off the ground, I don't know if that means she has some discomfort, which a therapist could identify, or it's the beginning of a contracture, which a therapist would catch right away, or even something else.
Hydrotherapy is not the only modality available. For example there is cold laser, which is good for pain, and e-stim, which helps with nerve recovery. Nothing is required of the pet for either therapy except to just lie still. No exercises or weight bearing. Swimming would also be non-weight bearing. The underwater treadmill involves bearing some weight, but how much depends on the height of the water, and it's less than walking.
After a possible unknown mishap at the vet (when they sedated her and she came home limping) I was feeling cautious about recommending she be taken somewhere else and handled again, but that is a judgment call you can make when you decide how you feel about the rehab therapist and staff in that department. If I were in your shoes, at this point I'd been feeling overprotective and they'd have to assure me they can work with a sweet senior cat at her pace (but that's just me).
My experience with hydrotherapy is with 2 dogs. The sessions start out short. The first few times you go the pet is only in the water for a few minutes. You may even wonder if it was worth the trip. But they build up gradually as the pet gets used to it, to avoid stressing the pet. Hydrotherapy would let her preserve some muscle mass and overall conditioning without having to bear weight, when it sounds like she doesn't want to.
I don't know about your rehab clinic, but a lot of places have appointments where you can pay per appointment, or you can pay for a package which is a set number of appointments, and it is more affordable. The first appointment will likely cost more as it takes longer and they evaluate the pet.
I tried 5 sesssions of acupuncture with my newest paralyzed dog. I could not tell whether it was doing anything or not, so we quit. I ended up feeling about 55% maybe it helped a little and 45% it didn't help. The acupuncture vet wanted to add herbs and said my dog wouldn't get the full benefit without them, and I declined supplements because he has a swallowing problem. We were doing it for recovery from quadriplegia, not pain. There may be better results when used as a pain treatment.
You were talking about whether to let her loose in the house. That's another judgment call and I'm not sure there is a definite right answer. It seems like if she isn't wanting to bear weight on that leg, then she might be better off resting. Muscle does come back when the nerves improve, which can take time, but that is referring to the affected limb or limbs, whereas you are concerned about overall deconditioning, and I don't know the answer. If it's a disk problem she'd do better resting. If it's arthritis then she's better to keep moving, with low impact exercise. If it is arthritis, the heating pad might be worth a try. She will know whether it feels good to her or not. Heat is good for arthritis. It helped my Betsy loosen up and do her grooming.
When the neurologist said she could do stairs again, the way I understand it, that was based on the assessment at the time that she was doing well. It seems like something has happened in the interim, and that advice might not apply now. Maybe you could get a recheck with the neurologist and see if it still holds. That would be another idea. Discuss what's going on, tell him she was doing better, you don't know what happened, and you're looking for any positive steps you can take to help her recovery. If appropriate, ask for a referral to try rehab. If he says again, "She may not like it," a good reply might be, "What can it hurt?" That is
advice someone gave me once, and it was priceless.
EDIT TO ADD: The oncologist might need to approve e-stim or cold laser, I'm not sure.