There are plenty of free polling tools which easily allow for conditional questions. I think these are vital:
I was previously infected with Covid
If yes:
With a positive PCR or antibodies test
Based on symptoms without a confirming test.
Agree, those would be needed for thorough survey.
Disagree, that those should be included in initial survey. Rather wait for first results, then create survey for whichever category is of interest, eg, if the "definitely not" category is huge, a followup might ask about the different reasons for being anti, where "prior confirmed covid" and "prior suspected covid" are some of the choices.