Business liability insurance would be needed, I think. If you set up one business entity, that covers all your side lines, you could just get one line of insurance. Note, I don't have business insurance.
Alternatively, if you are acting as occassional in-home help, like home cleaning, baby sitter (in their home), mowing lawns or even dog walking (where you pick up the dog at their place), the homeowner's umbrella liability covers injuries to personal workers...
To do this, I would make it clear to the client that their own home owners umbrella insurance would cover damages beyond your fee. You limit your coverage to your fee only, etc.
E.g., my own insurance covers a house cleaner working in my home when a bookcase falls on her. As a home owner it is up to me to demand proof of WCB and other insurance for home services contractors I have hired, if I don't want to cover them myself.
I am not an expert on insurance! Let's see if we get other, better, responses.