There's an option to install the "bash" applet as a link to either ash or hush, the two shells that busybox comes with. Turns out that a large number of "bash scripts" use no bash-specific features in spite of using "bash" in the #!, or only a few bash-specific features like [[ ]].
It's disabled by default, and arguably not a good idea to enable it because compatibility is not great as you found out. Either way, "busybox bash" doesn't exist: only the option to alias ash or hush to bash.
The bash you're seeing is a symlink to busybox, as are all busybox applets.
You can configure busybox to install an applet named "bash", but it's not a full bash shell. It's basically busybox ash, with maybe a few bash-specific extensions implemented. For example, it doesn't support arrays; `arr=(10 20)` will give you a syntax error.
In a default configuration, there is no "bash" applet. You can optionally configure busybox to alias "bash" to either "ash" or "hush" (and likewise for "sh"). This allows the use of "#!/bin/bash" scripts, but only if they don't use bash-specific features not supported by busybox.
I see it in the screen capture.
https://frippery.org/busybox/index.html