Is the saying "taking your time" or "she takes her time" idiomatic or metaphorical?

I would say it is both: a metaphor that has become idiomatic.

I’d say it’s idiomatic. Metaphors involve a kind of analogical thinking that doesn’t seem to be present in this expression.

I assume “taking her time” is somehow derived from take having the sense of require, as in “it takes her half an hour to get ready”, which I would say is neither metaphoric nor idiomatic.

“taking her time” as in, “she goes about [her task etc..] with a nonchalance…”

“When would you like me to have the paper completed Professor?”
“Oh, take your time. No need to rush.”

As in…“She takes forever to get stuff done”?
It can be used as a negative, “He just takes his sweet time no matter who’s waiting on him.”
Or if a person is struggling one could say, “It’s OK. Take all the time you need,” to reassure them.

No it should not imply a requirement for more time, or a need in general for time per se… But the choice of having the amount of time you would like [to get it done well] or [get it done with less stress etc.]

I think that these different interpretations are acceptable uses though! I had not thought of the other potential uses…

Well, take your time and think of some more. ;)