Is a Covid Recovery Letter needed?

QUESTION….Although I am fully vaccinated, Pzifer and boosted, I had a mild case of covid the beginning of January 2022, we travel in late May 2022. Self test, shows negative now.
Do I need to get a recovery letter as well to cover myself? Or does the recovery letter only pertain to those not fully vaccinated and recovered? When checking the official SXM Travel requirements it says:

Travelers who have recovered from a Covid-19 infection within 9 months before departure must upload one of the below acceptable proof of recovery:
*A government / public health authority issued proof of recovery (Digital Covid Recovery Certificate or letter)
*A lab issued positive covid-19 PCR test result also indicating a Ct value of 35 or higher.
*A signed and stamped Covid-19 recovery letter from a physician accompanied by the positive Covid-19 PCR test result.

Maybe I should just get a letter or test to be safe if I cannot get an answer.
All answers appreciated.

I’m making my second trip home next week with the doc note and a copy of the home test showing positive. No need to test if within the 90 days to return to the US. To enter SXM just fill out the EHAS and provide vaccine info. Don’t confuse them with COVID letter b

I agree....just upload the Vax info