Can a Simulacrum of a sorcerer regain its sorcery points?

The description of Simulacrum states:

The simulacrum lacks the ability to learn or become more powerful, so it never increases its level or other abilities, nor can it regain expended spell slots.

If someone cast Simulacrum on a sorcerer, would the Simulacrum be able to regain its sorcery points by taking a long rest? (Can simulacra even take rests?) In particular, I ask because the sorcerer has the Font of Magic class feature at level 2 that allows them to convert their sorcery points into spell slots or vice versa.

(This question can also be extended to other limited-use class features like a fighter’s Action Surge, a druid’s Wild Shape, etc., but I don’t know if the answer would be different since sorcery points can specifically be used to create spell slots.)