Haven't tested it out on the hardware but I think that one of the two examples down below would be a good place to start.
The first I'm not sure will work as it won't store the value, but I'm trying to incorporate the manual pressing of a button, perhaps a table would work, I'll have to think about that a bit.
The second example is more automatic, when the program change is received the program number that is sent out by the digitakt will send a value and a trigger, then the value gets your +1 and a delayed pulse send the trigger after a delay to the program change midi out.
From memory if the digitakt receives a program change message it will not act on it until the current pattern cycle is over, so the delayed pulse should be effective. (really it would be the same as pattern chaining but would just automatically select the next pattern up, if it works)
As I say I haven't tested any of this and things like your Auto channel (on the Digitakt) should be the same as on the patch in my example channel 14 which I think is the default. Theoretically you could use Midi Loopback via the Axoloti and achieve something similar with a Digitakt midi track and a midi thru on Axoloti