This is a gem of an app that turns your android phone into a Bluetooth mouse and keyboard for other devices.
Edit:
What makes this app different from other “remote control” apps? Most of them need a “server” or “companion” app to be installed on your other device. This app doesn’t. It just needs pairing via Bluetooth.
I use it to control an Android tv box. As you know typing with on-screen keyboards on tv screens is an absolute pain.
With this app you can type anything on your smartphone and send it to any text field on your other device. You can also add cistom keys and key combinations. Note the CTRL+A shortcut key i have added for select all in the screenshot for example.
It can also work as a mouse with customizable buttons.
https://play.google.com/store/apps/details?id=io.appground.blek
As an alternative, you could consider KDE Connect. It does a lot more than just keyboard and touchpad. You can even send files both ways extremely quickly.
It looks like you have to install KDE connect on both devices, and they have to be on the same network. Handy, but completely different type of app and method of execution.
There are a slew of Android TV remote apps that do all this and more, like including home/back buttons, integrated search etc. They also pair easier. The first party Google TV app covers this smoother than a BT keyboard/mouse app.
Most of them need a server app to be installed on the other machine. This app needs no server or companion apps.