TDA2040 transistor short circuit
(1)  Could it be damaged?

Yes. The fact that one channel is now much quieter than it was before would indicate that damage has been done somewhere in the circuit, though not necessarily in the IC.

(2) could I better change them both with TDA2050?

(3) putting a diode in the supply feed



Swapping for a different amplifier is up to you. Comparing the tda2040 and 2050 circuits they are pin compatible but you may need to change a couple of RC values.

Adding diodes into the supply feeds would introduce a voltage drop. Depending upon current this would be in the range 1-2V for each diode.