Update: the sandbox ended up finally getting deleted. All told, it was stuck in that "Soft Deleting Failed" status for around 48 hours. Thanks to everyone who responded with suggestions.
I am curious as to whether anyone else has run into this issue. I attempted to delete a sandbox environment in my CDX tenant via the Admin Center. Per usual, the environment was placed in a "soft deleting" status. This operation ran for about 20 minutes, after which it updated to "soft deleting failed." The operation details suggested I run the operation again, but subsequent attempts have also resulted in failure. The details also suggested I contact Microsoft support, but I've been bounced between a few different support accounts at this point, with each one essentially responding "not my issue."
I haven't found much information on this online; what little guidance exists suggests to restore the environment from the "Recently deleted environments" list and then try again, but my issue is that the environment is stuck in a soft deletion failure, so it never makes it to the list of recently deleted environments.
So now I have this Business Central environment that's stuck in a weird limbo that I can't do anything with.
A screenshot of the operation details is presented below.