Be sure to appreciate the difference between "com.apple.developer.submerged-depth-and-pressure" and "com.apple.developer.submerged-shallow-depth-and-pressuer" (note with the -shallow- in there)! The "full" one is apparently the one that will require special approval by request; the "-shallow-" one is apparently more "public". For others who are reading this: also note that any "old" (mine was from some months ago) Provisioning Profile will have to be re-created. That is, re-created using a distribution certificate (or development certificate?), which in turn needs to be (re)created from a Signing Request plus App ID, such that your App ID may need to be (re)created because that's where you check the Capabilities boxes; including the "Shallow Depth And Pressure" one. Probably seems obvious to others, but I didn't know that Capabilities were something that had to be set up in App Store Connect.

I, too have run into the same problem (same error; I expressed interest; no reply yet) and am very close to being otherwise finished with my app. I am about to use a support incident to nicely ask about this.