Is there widely accepted phpDoc syntax for documenting which hook calls a function?

Function doc block should document what it does, what it might be useful for, but not who uses it. It makes sense to document that it was designed with hook X in mind but that is it.

Think of unit testing. In that context you are likely to call the function by itself without doing the whole core initialization, which means that a description tying the function to the init hook, will be at least misleading.

The style you are trying to use will also force you to change documentation while changing irrelevant code, like if you will decide to move the call to wp_loaded instead of init