Almost everything falls into one of three buckets: the pairing code did not work, the library is not awake, or the phone and the library cannot reach each other on the network you are currently on. The sections below are in the order worth trying.
One question tells you a lot before you do anything else: does it work at home but not away, or does it not work anywhere? Those are different problems with different fixes.
Expected, and not a sign that anything is wrong with the download. The installers are not code-signed yet, which means your computer cannot confirm who published them and says so rather than staying quiet.
Only override a warning like this for software you deliberately went and downloaded. Get the installers from the releases page and nowhere else. Signed builds are planned, and these prompts stop once they ship.
Pairing codes last a few minutes and are meant to be used once. If yours is refused:
If the code will not scan, raise the screen brightness on whatever is showing it and clean the phone's camera lens. Failing that, copy the pairing link shown under the code and send it to the phone by any means. Opening that link, or pasting it into the app, pairs without the camera.
This is the interesting one, and it usually is not the app. On your home wifi the phone and the library can find each other the easy way. From outside, they have to make a direct connection across two networks, and a small number of networks will not allow that.
Things worth checking, roughly in order:
The app says which libraries it can currently see, and a library it cannot reach is greyed out rather than hidden, so you can tell "not available right now" from "no longer mine".
The library builds an index of your music so the app can browse it quickly, and files added since that index was built are not in it yet.
Track down whether it is the connection or the file.
Make sure PearTune is installed first. A link tapped before the app exists has nothing to open it. Install the app, then tap the link again, or copy it and paste it into the app's "paste a link instead" box on the pairing screen.
Email peerloomllc@proton.me or open a GitHub issue. Include the phone model and version, what the library machine is, whether it fails at home or only away and what you have already tried.