It's a bit weird and nobody knows. Try moving this to Coronavirus section OP as you might get more answers.
I haven't had Covid but I am on the mini pill. Never any issues apart from the extremely rare case of forgetting to take at the same time and then I get very light spotting for 1, maximum 2 days. Otherwise no periods ever.
After 2nd vaccine I kept getting random light periods so I actually stopped the pill to see if my normal cycle is OK. It was as normal, regular, no issues. I am not peri menopausal and don't have any health problems, always had very regular, trouble free periods. After 3 cycles I started the mini pill again. All good, no bleeding.
Had my booster and since then I often get light bleeding, not just spotting. At random times. And I take the pill at the same time every day to the minute.
All 3 vaccines were Pfizer.
I suspect something happened in relation to the vaccine but can't prove anything and I might just stop taking the pill for a few months because this whole thing is very annoying.
As an aside, at my first vaccine, I specifically asked a doctor if there are any issues associated with taking the pill, if there are any extra precautions I should take. He said no, carry on as normal, there is no interference between the two.
I think having an illness or stress does affect periods. But more in the sense that they stop temporarily. Maybe they just go out of sync. It may be true of contraceptives too.
I have zero proper medical knowledge though.