This small business is not allowed to let customers enter the shop if they can't validate their vaccination status. To do this one needs a QR code reader on a phone. Practically speaking there are no alternatives.
Also, they're not saying that your business needs to run this app, they are saying that your business needs to verify Covid certificates and offering these apps as one way to do it. But it's not the only way - for example, it may be less convenient, but you can do that QR code scanning + Covid certificate validation on any computer with a connected camera using a web service (https://app.digitalcovidcertchecker.gov.ie/ is one random example, there is also open source code to roll your own checks for EU Covid certificates in some custom system if you need to), and there you can use Windows or Linux or whatever, there's no need for a smartphone as such. In fact, if the parent poster's Pinephone can run a browser and expose a camera to it, then perhaps it might work out of the box on the Pinephone without needing a special app.