I hate common names for plants. They do nothing but lead to confusion.

Broom Sage is a good example.

Is it really Sage, as in Salvia?

Or is it Broomsedge, which isn't a sedge, but an Andropogon.

Can you grow it in your kitchen garden? Probably, if you can decide which of the hundreds of plants it could be, is really Broom Sage.

But why? Terra Cotta pots won't restrain it, because it self-propagates by prolific seed production and has a high germination rate. If you dead-head it before the seeds ripen, you lose the ornamental quality.

Buy a broom at Wally World and grow good stuff in your garden.