Ventura docs for M2 Macs in this comment: https://gist.github.com/henrik242/65d26a7deca30bdb9828e183809690bd?permalink_comment_id=4555340#gistcomment-4555340
Old Monterey docs in this old revision: https://gist.github.com/henrik242/65d26a7deca30bdb9828e183809690bd/32c410e3a1de73539c76fa13ea5486569c4e0c5d
Solution for Sonoma: https://gist.github.com/sghiassy/a3927405cf4ffe81242f4ecb01c382ac
No, the error talks about an error with apsd's connection being interrupted. This is for Apple Push Services Daemon which means you might not get push notifications on that system, but that doesn't mean a profile could not be installed. The response you should get if DEP servers are blocked is similar to below:
Error fetching Device Enrollment configuration: (34006) Error Domain=MCCloudConfigurationErrorDomain Code=34006 "The Device Enrollment server is unavailable. Please try again later." UserInfo={USEnglishDescription=CLOUD_CONFIG_MAX_RETRIES_EXCEEDED, NSLocalizedDescription=The Device Enrollment server is unavailable. Please try again later., MCErrorType=MCFatalError}