I just installed the latest version enabling the "jammy" repo (the one that has 0.52-1), and the result was the same, no DSP using Jack. No luck so far :(
But great that you tried it and hence gathered more information about your problem. You know that you can increase Pd's debugging level and/or start it with the -verbose flag to get more detailed error messages. Does Pd post anything there when you start DSP?
On the jackd side: Are you getting any messages from jackd, for example by looking at qjackctl's "Messages"?
And do you have a second alternative sound card you could try?
cheersz, P