UPDATE
Can you add precheck to a ticket you've already booked? Where do you do that?
Being that I only got approved for precheck after I booked a few tickets, I wanted to try to add my number in retroactively. For a flight on AA, I was able to login to my reservation and add my "known traveler number" in there. I called up AA and they confirmed that my number was in the system and would be on my boarding pass. Sometimes you
can trust a CSR because TSA PRECHECK printed out on my boarding pass! On the plane now after having enjoyed my first precheck (besides for 2 times I was randomly selected for it).
I also have a SW ticket that I booked before being approved for precheck. I was able to add my number to my SW RR profile, but I could not add it in to the actual reservation. I called SW and they told me it's not on the ticket, but they gladly helped me add it over the phone. Hopefully everything goes smoothly when I get to the airport.
Data point for the timeline here: I had my interview and was approved for precheck on Motzai Shabbos, got my confirmation email later that night, and my number worked for a flight I took Wednesday morning.