I've found out why. I had JDK (Java Development Kit) version 7 installed, but I should only use 6 or 8 (really 8, because 6 is super old).
On Manjaro (or any other Arch-based Linux distribution) what I had to do was to install the
jdk8-openjdk package and then check out what files it installed.
I was mislead by the fact it didn't put anything into
/usr/bin - so I was unable to locate the jarsigner binary at first. But it's there. It's full path was
I've put that into Godot's Editor Preferences and it finally was able to sign my APK.
Another note regarding One-Click Deploy - you don't have to install Android Studio.
You just need
What I had to do was install the
adb package and then run
adb devices command.
This triggered my phone and it asked me for permission to allow my PC to connect via adb.
Only once I have confirmed that did Godot show the One-Click Deploy button, because it had access to my mobile device.