Personally I’d be reluctant to blame the DECT phone as the filter within the NTE would, if it were perfect, render the DSL side immune from phone faults, especially if the phone is basically working and not totally kaput. Filters are not perfect of course so it still might be the phone, just on balance of probability, I’d want pretty compelling evidence before splashing out on a new DECT phone.
With the analogue phone, have you tried an incoming call, leaving it ringing for a while, to see if that might have detrimental effect?
Another point, DECT phones often have rather noisy PSU bricks. I assume the wiring to the modem is well away from the phone’s power unit?
You can’t really rely on noise symptoms from a digital phone as it might be internally generated, but even so, noise that starts of loud and then fades, might be more suggestive of a line fault.