All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The verse that you mentioned, which is the saying of Allah (which means): {…And when you ask (his wives) for anything you want, ask them from behind a screen, …} [Quran 33: 53], addresses all Muslim women even though its words are peculiar to the wives of the Prophet . This is the opinion of the Muslim scholars.
Here are some of what they said about this:
Al-Qurtubi (the great interpreter of the Quran) said: “This verse is an evidence that Allah has granted permission to ask women for something when screened from men if there is a need to do so or if one is asking them about something related to religion. All women are included in this ruling. In fact, the fundamentals of the Sharee’ah consider the whole body of the woman an ‘Awrah. Her voice is an ‘Awrah as mentioned earlier. So, this should not be exposed except for a legal necessity, like bearing witness, or seeking cure from an illness in the body, or answering questions about things that are usually peculiar to her.”
Ash-Shawkaani who is another interpreter of the Quran, said while explaining this verse: “And this is a kind of ethic for every Muslim and it is a warning against being over self confident as far as staying in seclusion with non-Mahram women, or talking to them directly without a Hijaab.”
On the other hand, what is the difference between the wives of the Prophet and the other Muslim women as far as this issue is concerned? If the women who were educated in the home of the Prophet are addressed as above, and those who talked to them were only the honorable companions of the Prophet then other women are addressed even more emphatically.
For more benefit that a woman's voice is not an 'Awrah, please refer to Fataawa 263791, 82218, and 83899.
Allah knows best.