Hi Leonard, A few things might prevent Bluetooth detection and connection. We have new Bluetooth extensions that work smoothly, and every tutorial from fall 2022 is current.
For your UART-based project, I would start by loading the Microbit and App Inventor templates located in our Project 2 tutorials, and then modify to your needs. The templates have a nice event-based structure for sending data.
Here are the files:
Setting up the Microbit (this hex code for Microbit will adjust the settings in the MakeCode IDE)
Setting up App Inventor (this contains the latest UART extensions)