giuliomoro
I have searched for the breakout datasheet but sadly I'm not able to find it.. Only the chip: https://www.ti.com/lit/ds/slos708e/slos708e.pdf

Pseudo-differential output
giuliomoro is the TPA3118 module's input fully differential? If so, as you have spare channels you may generate pseudo-differential outputs (i.e.: where the R output is the opposite (* -1) of the L output) from a stereo pair and then connect L out to the + input and R out to - input and see if that works.
I tried connecting the signal wires (red and white) to INPUT+ and INPUT- and sending the same output to both, but phase inverting one of them. I tried with ground going from the step-down converter to GND pins and audio grounds. In either case this produced a lot of noise until I touched the INPUT- with the Audio GND wire, which muted all sound. So I guess my breakout board isn't setup to use the differential option and either the RINN or LINN on the chip isn't used for input (see section from datasheet below).

FROM CHIP DATASHEET:

PATCH FOR DIFFERENTIAL TEST:

Nothing to INPUT- AND INPUT- to Power grounds
giuliomoro You can also try to connect nothing to the - input, or connect it to the on-board ground instead of bringing the ground across from the Bela Mini.
This produced a lot of really loud noise! 😃