Digitakt doesn’t turn on because it may go in some kind of protection mode when it turns off due to lack of power. Just leave it charging for 20 minutes then turn on Digitakt with PSU in. It will be charging and working off PSU easily.
In general, this doesn’t happen and as soon as you insert the power supply, it should switch back to it. I noticed this behavior only when the battery is discharged below some critical level. Then the fix is as I mentioned — leave it charging with Digitakt off for 20 minutes.