We had the same questions that you have when we traveled back in October. We were trying to decide on local pharmacy testing vs the Abbott BinaxNOW home test with a proctor. Based on the advise of many on this forum we did decide to use the Binax in our hotel with a back up plan to schedule an in person test at a local testing center if the self testing failed. It really was an easy and convenient method to meet the requirement.
I ordered the six pack of tests, downloaded the NAVICA app and set up our accounts at home. We did do a test at home for two reasons, one, to make sure we understood how the whole process worked while still able to get questions answered, and two, I wanted to be confident we were negative before leaving the country since I am a nurse working in a hospital. Got the tests emailed within minutes and felt confident of the entire process.
In order for the test to be accepted by the airline to fly home to the US it must be proctored, done on line with someone that can scan the code on the test package, your picture ID, and the result card. The test result is easy to read, but the proctor views and verifies and sends an email within minutes. We then forwarded the email to the hotel’s front desk and they printed for us.
You could easily do the test without any proctor, but the results are not recorded anywhere. Thus nothing to show the airline. Most likely the test your library is providing. Six tests are quite a few, someone on this forum said its possible to order only a two pack. We wanted six tests, two for testing prior to our trip, two for testing to meet the airline requirement and the last two for a planned trip to the Christmas markets later this month. Well sadly that trip is now off but there is always next spring and those two tests are ready and waiting.
No matter which method you use, local pharmacy or the proctored test, there is a cost to getting a test to fly back to the US. Will most likely be a part of the travel process for the foreseeable future for quite some time.