Hello Glenn Horton,
I've reproduced the issue with the same VM config as follows,
Even for me also at the beginning the ASR mobility service was not running.
I tried restarting the service and checked the Microsoft.SqlVirtualMachine resource provider status & re-registered it.
Follow the below steps.
Despite having these things ready, the rollup 62 which supports the OS & kernel (RHEL 8.6 4.18.0-372.113.1.el8_6.x86_64) has some known issues related to Installation of mobility service, as it was becoming unresponsive due to an internal operation incorrectly handling null parameter.
Refer to the below doc. https://support.microsoft.com/en-us/topic/update-rollup-62-for-azure-site-recovery-e7aff36f-b6ad-4705-901c-f662c00c402b
So, try restarting the service again and enable the replication then check the extension status over VM blade as below and keep tracking the replication status. FYI, I have followed the same and succeeded with the replication.
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Thanks.