The core integration for Anthem AVRs is missing this, but it has been implemented in a custom version of this integration (see here).
It looks to be a pretty simple change to add this to the core integration.
I might have a go at doing it myself…
Hah, I stumbled over the same thing. Here’s a PR to implement volume control: anthemav: Add fine-grained volume_up / volume_down controls by antifuchs · Pull Request #137499 · home-assistant/core · GitHub
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