Hi - I wanted to add another anecdotal experience about pre-flight COVID testing, also flying United.
I initially booked an appointment through United's recommended Trust Assurance - which would have allowed me to visit a local Quest laboratory for a COVID PCR test. The cost would have been $139. However, I had also bought two at-home proctored rapid antigen tests, which I originally read about on Cameron's blog. And, since at the time the testing requirement was 72 hours prior to arrival in Italy, and this gave me time to try the at-home proctored tests, first, before committing the the Trust Assurance test (having read this thread about the wife's result being delayed).
Proctored means that you connect virtually (like a tele-health visit) with a trained "assistant" who observes the entire process of you doing the nasal swab sample collection on your self. Went very smoothly - I cancelled the Trust Assurance appointment in time for a full refund and saved myself quite a bit of money.
Tips for the at-home proctored test: Follow all instructions carefully, including: 1) Download the accompanying app (in my case, called NAVICA) to your phone first, and create an account - be sure your name and date of birth match your official travel documents. 2) I used my laptop to actually make the video call to connect with the proctor. You should have a clean, flat, clear space on a table available, and then be prepared to tilt your laptop screen down to show the entire space. (I think it helped that I had done an unproctored at-home rapid antigen test once before, so I knew a bit what I was doing already.)
I waited maybe a minute for the proctor to come on. They can see and hear you, but you only hear their voice. Once the test was done, I set a timer on my phone for 13 minutes, and came back to my computer so that I would be waiting for the proctor when the 15 minutes ended. When the second proctor came on to verify the result, I could not hear her, though we could use 'chat' with each other. She briefly disconnected and came back on and her audio was restored, no problem. Once complete, I had the test result on my phone in the NAVICA app within minutes. I also accessed the emailed test report, saved it as a PDF and then used the PDF to upload it to the United Travel Ready center using my laptop on the United website. Within a few minutes, United had "approved" the COVID testing documentation. Once you check in for your flight (which you can do at 24 hours before departure), be sure you can see the GREEN "Travel Ready" mark on the boarding pass in the United App on your phone.
My flight leaving the US was delayed for a bit more than an hour. As far as I can tell, the delay was for two reasons: 1) wheelchair assistants who were late helping individuals who needed assistance to the plane, but 2) perhaps the more significant delay -- listening to the gate agent who was frantically/frustratedly speaking to all the passengers through the loud speakers at the gate, and given the length of the line that formed to remedy the issue -- was that people who were using the United App did not (apparently) have the "Travel Ready" green mark on their boarding pass. Again, I only used the United App for my boarding pass. I could see the green "Travel Ready" mark, and I had no problems at the gate.
Remember, the United App will not show the green Travel Ready mark until all the pre-departure documentation has been verified, which includes (1) passport and (2) negative COVID testing documentation approvals, and (3) the "normal" flight check in process.
Hope this is helpful.