A prayer area in a home or workplace does not have the ruling of a mosque

If a woman has a specific place in the house that she cleans and where children do not enter, so that she can pray in it, does it have the ruling of a mosque? For example, when entering it, does she pray two rak'ahs or perform i'tikaf (spiritual retreat in the mosque)?
A prayer place, whether in the house, a government office, a company office, or elsewhere, does not have the ruling of a mosque; rather, it is a prayer place, just as a person prepares, for example, a carpet to pray on, which does not have the ruling of a mosque.