This was really confusing to me too. We recently flew into Edinburgh from the US, fully vaccinated. We had a busy road trip planned - 1-2 nights in each town, no “home base” to send a CTM test.
We pre-booked appointments about 1 hour after scheduled arrival right at EDI. It was 99 GBP each.
The test center is an approved one, but the confirmation numbers they gave us had a different prefix than what was accepted by the Passenger Locator Form. You can’t finish the PLF without your Day 2 test confirmation number.
It was stressful. I had to check the test center FAQ to get the proper prefix and number format. But it all worked out.
For our return to the US, we made appointments at Hawkes Health in Dundee (one of the sites listed on the Us Embassy page for Scotland). We got antigen tests for coming home, and that was fine. They were about 50 GBP - much cheaper than PCR tests.