I have played a fair bit of Java MC on my phone and can confirm Pojav Launcher is legit, HOWEVER

• That website you linked is bogus. A lot of Android projects end up plagued with malicious websites like this one. The only proper place to download it is their Github.
• Visiting their GitHub page, you'll see Pojav got discontinued, and that you should get their succesor instead: Amethyst.

As their README says, download it by visiting their nightly.link or by going into the "Actions" tab on their GitHub.

Remember, only download it from their official GitHub page, don't trust those shady websites from the Google search.

I run MojoLauncher which runs better than Pojav Launcher. It's a bit laggy, and the default control map was no good so I had to customise it to be better, but it does work.

It's worth noting that the full version of Luanti runs natively on Android, is fully free, and plays fully cross platform will all Luanti servers and other copies of Luanti.

One Android phone copy of Luanti can even serve the game to a few other players playing on PC or Android.

I can't help with how trustful this is. There is also MojoLauncher, that is based on PojavLauncher: https://mojolauncher.com/ There is not much information and I would be very careful. It's not even on F-Droid.

I found Cuberite on F-Droid: https://f-droid.org/en/packages/org.cuberite.android/ , it's website: https://cuberite.org/ and source code on Github: https://github.com/cuberite/cuberite Is this trustful? Looks more trustful than the others. I'm not sure if this is the kind of app you are looking for, it's description is " A lightweight, fast and extensible game server for Minecraft Java Edition ".