At least this is quite normal; any CD player should output exactly the
same data, regardless of it being a high end tabletop player or portable one

The SQ difference lies only in the DAC and the analog stage, in my opinion...
As for the DM13 in BT; I just tested on 3 devices: on SMSL AD18 FDA it works, the DM13 says Apx but there are random glitches in the sound. With my Focal .Listen Wireless headphones, it connects , no glitches but no codec display: the Vxx volume indicator blinks...
And last but not least, with the Qdelix 5K forced to Aptx HD it works fine, see pics...

[EDIT] Works very well also with SMSL RAW-MDA1 dac...
But it resamples to 48 Khz... very weird for a Cd player, which is supposed to output 44.1Khz by definition