I'm in a similar situation - COVID-19 resulting in an ICU stay, then the vaccine (Oxford-AZ) - and I figured it couldn't hurt (read: was extremely unlikely to cause major side effects) and _may_ confer some slight benefit (similar to mixing vaccines or just renewing my immunity). Vaccine passports were also being mulled around that point, and I assumed it would make that process easier if necessary.

In the end, I did get some side effects, but nothing long term - a hard, hot to the touch, red circle of about 4" diameter formed around the injection site, and I could barely move my arm away from my body without significant pain, both for about a week.