Arduino Mega resets when DFPlayer speaker plugged into amp!
For externally amplified speakers, you should be feeding the DAC and GND pins to the amp's inputs.  Those DAC pins provide a signal that varies by a small number of volts and is shifted so that they're always positive.  This is in the range expected by small headphones (ear buds) and line level inputs to audio components like an amplifier.

The speaker pins on the DF Player mini are pre-amplified (a little tiny bit) to directly drive a very small speaker (like 2 Watts at 8 Ohms).  They are a differential signal that includes both positive and negative voltages (relative to GND).  Note that the two speaker outputs (SPK+ and SPK-) are not left and right, but two sides of a differential signal.  Based on the schematic on page 11 of the datasheet (Chinese), it's a mono output made from mixing the outputs of the left and right DACs.

I could see how you might have gotten away with sending those to the amp, since the pre-amped speaker outputs are low power, and a good amp probably has input protection.

I don't know enough about electronics to know why it's failing now when it seemed to be working before.  It could be sensitive to the amplifier's gain or a ground loop between the power sources, but I'm just shooting in the dark.  Somehow, I suspect the DF Player Mini struggled to provide enough current to your amp, and since the DF Player Mini was powered from your Arduino, the Arduino essentially browned out, triggering a reset.