Fatigue and depression following COVID-19 in a Parkinson’s patient

Hey people,
I wonder if any of you can share some advice, ideas or insights here:
My father, who’s 76 years old, suffers from Parkinson’s for the last 1.5 years and is treated with Rasagiline (Azilect). He recently had COVID-19. The acute disease stage was flu-like in symptoms and severity (so, no fun, but not too bad either; note that he got Paxlovid starting from the 3rd day of symptoms). However, even though he recovered from the acute COVID stage more than 2 weeks ago, he still suffers from severe fatigue, and the depression he had (one which he refuses to admit, unfortunately) since having Parkinson's has gotten much worse after COVID (plus, I suspect he may have become apathetic, but I'm not sure I can differentiate between depression and apathy). There are other changes (e.g., worsening of the slowness of movement, post-exertional exhaustion etc.), but I find the fatigue and especially the depression/apathy the most troublesome.

I should mention that we are from Israel and that my parents came back from a trip to California just 24 hours before finding out they had COVID (my mother was almost asymptomatic). So, they were, indeed, jetlagged (there’s a 9-hour difference), but it has been some 3 weeks since they got back and, nevertheless, my father still goes to sleep in the middle of the day (for a few hours), and his nighttime sleep is poor – he gets up at around 3 a.m. (instead of 8 a.m.). Importantly, up until 3 weeks ago he practically never slept during the day, and never had major sleeping issues at night. I suspect one reason he goes to sleep during the day now is that he became depressed/apathetic and, because nothing interests him anymore, he has nothing to do, so he goes to sleep.

I'd love to hear some of your thoughts. In particular, I wonder what you think about the following (based on your experience, things you've heard of, or anything else):
1. Do you think it's likely that these symptoms (that started/worsened with COVID) will resolve/improve on their own?
2. Do you think changing the Parkinson’s treatment (e.g., starting him on levodopa) can help? Note that, regardless of the post-COVID deterioration, I suspect (though I can't know for sure) that the impact of the Rasagiline on my father's symptoms (motor and non-motor) is mild at best.
3. Do you think some other, non-Parkinson's-related type of treatment can help him? What about some kind of stimulant (for instance, Provigil), to at least keep him awake during the day and get him to be more energetic?
4. I really want my father to start taking anti-depressants, but the problem is that he won't admit he is depressed. Also, my mother says the very suggestion of it would really offend/sadden him, so I'm worried about even trying. Do you know if there is any type of antidepressant (or even a medication not defined as an antidepressant, but that can nevertheless help improve one's mood) that is sometimes used to treat any type of Parkinson's symptom that is more "physical" (tremor, slowness, even sleeping problems...)? Because he will agree to take it if the doctor says it's for physical symptoms.

Best,
Omer