How to use the `$HOME` environment variable in systemd service files

I think this is what you're looking for: https://www.freedesktop.org/software/systemd/man/systemd.unit.html#Specifiers.

Specifically, %h should expand to the current user's home dir.

The full list of supported variables (called "Specifiers") is here: https://www.freedesktop.org/software/systemd/man/systemd.unit.html#Specifiers.

There is no specifier for the home directory of user the service is run as (the one specified by User=). There is only one for the user running the service manager.

From the link:

%h is the home directory of the user running the service manager instance. In case of the system manager this resolves to "/root". Note that this setting is not influenced by the User= setting configurable in the [Service] section of the service unit.