Do X.25/Frame Relay/ATM/MPLS have their own isolated physical infrastructure? Or are they technologies invented to utilize the then existing infrastructure of the PSTN?
Short answer: No, and no.
Long answer: At the time X.25, Frame Relay, and ATM were in widespread use, voice networks were still largely "circuit switched," meaning, a dedicated data channel was likely to exist between the PSTN switches terminating each end of a phone call. The PSTN inter-exchange switches themselves handled the circuit-switching.
The technologies you mentioned are all "packet switching" (or cell switching) technologies allowing for over-subscription. This is important when serving data terminals (such as early cash dispensers or finance applications.)
Those packet-switching technologies used some of the same underlying link-layer technologies as voice networks. For example, a DS1/T1 might've carried 24 voice calls or 1.5Mb/s of packet data.