Most orgs would not consider this staff-level work. Doesn't mean you shouldn't get your hands dirty every once in a while and it could even be helpful for "dogfooding" purposes but if that's all you ever do that's not Staff.

Yes and no.

I have been asked if staff engineers are around so that they can pick up projects noone wants to do. This entirely defeats the point of staff engineers.

I would want my staff engineering bunch to either pave the path or mentor the teams to do it themselves. Making it easier for the teams and future engineers could be a better strategy and effective multiplier.

If there is organisational mission critical software lacking any of this then it is a p0 and I would count it under high impact work rather than gardening. Besides depending on company size, some of those responsibilities should belong to platform teams.