Is there a good/standard way to find the equivalent to this part but for a different connector?
You want to find a different part with the same footprint.

Unfortunately there's no standards body regulating USB connector  footprints, and all digikey offers is "mounting type" = "Through Hole, Right Angle"

Type C has more than 5 cable pins, so fitting type C there is not going to work, USB 2.1 Micro B OTOH does have 5 cable pins so you just need to find a connector with the right footprint.

searching on digikey finds no suitable usb micro connectors,  all the right-angle micro connectors seem to use surface mount terminations for the data pins. you'll have to pick one that fits the mounting holes used by the mini socket and extend those pins to reach the pads that the mini socket used.