Personally, as a rule of thumb, I don’t think you can have enough in savings.
Our society is built upon going into debt… and I’d rather pay up front for things like a replacement vehicle or heater/pump or what have you, which means having enough to survive on—as you are inferring—and enough to survive Murphy making an unannounced and unwelcome visit.
Personally, I use ‘savings’ as a catch-all for any form of money you have no intention of spending frivolously. Be that in savings, stocks, or other forms of investment.
I’ve got a relative who saw anything beyond the 6 month mark as spending money. I don’t know what form his investments manifested in, but it clearly didn’t work as he’s in financial do-do, and it’s an unpleasant topic amongst the family.