I don’t think I have an answer for you, but most iOS-like devices have some kind of “DFU” mode where the lowest levels of firmware can be rewritten via a USB cable using iTunes or something similar (e.g. the Finder in Catalina).
I’ve done this with a 3rd generation Apple TV. There are similar modes for iPhones.
I would assume that there exists a DFU mode for a HomePod, but I haven’t found an article explaining how to do it or how to use it to replace broken firmware. It may require access to some internal connector on one of its circuit boards (e.g. a USB or a serial port connector of some kind).
It appears you can do a full restore to a HomePod mini by connecting it to a Mac via its USB-C cable. This is what you can do with a bricked device to restore it after putting it into DFU more (in addition to using it to restore the firmware of a non-bricked device).
Unfortunately, there doesn’t seem to be any user-accessible data port on the full-size HomePod, although iFixit found a hidden 14-pin port on the inside. I assume that this is a diagnostic connector that probably contains something like USB and serial I/O (and maybe even JTAG-based debugging) for use in the factory.
If someone could figure out the details of this port and build a cable to mate with it, I strongly suspect it could be used to trigger a DFU mode and install replacement firmware, but as far as I know, nobody has yet done so and Apple certainly won’t, so it doesn’t help us.