Travel to US from UK via Portugal – recently recovered from Covid

I am travelling from UK to Portugal with TAP on 22nd March, spending one night in Lisbon, then travelling to San Francisco on 23rd March. I recently had Covid (positive test on 23rd February) and am now recovered. I have proof of this recovery in my NHS Covid Pass app, and am triple-vaccinated.

Will the NHS app QR code be sufficient proof of recovery to enter the US?

This CDC page says

If you have had a positive viral test on a sample taken during the past 90 days, and you have met the criteria to travel, you may travel instead with your positive viral test results and a signed letter from a licensed healthcare provider or a public health official that states you have been cleared for travel according to CDC’s travel guidance. The positive test result and letter together are referred to as “documentation of recovery.”

I recovered less than 90 days ago, so I am ok there, but I am wondering if the app counts as a "signed letter" or if I need to get a physical piece of paper from my GP.