I flew in 2 days ago and can confirm no, they don't want to see it. You only need to show the qr code of the Thailand pass.
(When you get off the plane you go through a separate section where they scan the qr code and then stamp your boarding pass, that's what you then show to immigration)
Boarding the plane to Thailand required showing the Thailand pass AND proof of double vaccination.
I bought the 650 baht insurance 12 days before my flight...