Minimalism is a different thing. Living within your means is about budgeting, its arithmetic. Minimalism is about owning very few physical things, but often very nice things. Like only having 3 pairs of pants but they all cost in excess of $200 each. Basically it boils down to owning the just essential and carefully chosen artifacts or modern life.
Note, I'm not endorsing this idea, just trying to describe it.
Well, I suppose everybody is going to have a different opinion. To me, it's more about avoiding excess, mostly to keep spending down.
There's a certain level of minimalism though that actually increases spending. For example, not keeping a toolbox around the house means having to call someone for even the smallest maintenance work you might need.
You seem to be deliberately missing the point, if you need tools then keep them, the point is to own what's necessary rather than what society and marketers think you should.
Not keeping a tool box around the house very rarely means not having access to tools. Tools are commonly borrowed/shared amongst friends, family, neighbors, co-workers, borrowed from work, co-ops[1], makerspaces, or rented[2].