I've read that "‘Umar ibn al-Khatt?b said:“The foulest of women is the Salfa’.” Salfa’ is the immodest woman who mixes with men and is not shy from them." Is this authentic? Could you please elaborately explain about Salfa' from the scholars? Is a brave, outspoken yet modest woman (in clothing, manner, etc.) considered to fall into this category?

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.

We did not find the narration in the wording mentioned in the question. Instead, it is reported from 'Umar that he said in the interpretation of the words of Allah, the Most High: {Then one of the two women came to him, walking with shyness...} [Quran 28: 25] He said, “She came, walking with shyness, covering her face with her garment, not in a provocative manner, decent and chaste.” [Reported by Ibn Abu Ḥaatim and Ibn Kathieer authenticated it in his commentary].

Ibn Abu Shaybah, mayAllaah have mercy upon him, also narrated from 'Umar that he said: “A person has not gained anything worse after disbelief in Allah than a sharp-tongued woman with bad character.” Also, in a narration from Ḥanaad in the book of Zuhd from 'Umar : “No slave (of Allah) is afflicted with anything worse after disbelief in Allah than a sharp-tongued woman with bad character.”

In summary, what the language scholars mentioned about the meaning of the term as-Salfa' is that it refers to “the impudent woman who is bold with men,” and she is “the loud, impudent one with bad character” and “the shameless, indecent one with little modesty.” There is no doubt that this type of woman is the worst. Sharee'ah encourages divorcing such a woman, as stated in the hadith: “Three are those whose supplication is not answered by Allah - and among them he mentioned- a man who had a woman with bad character but did not divorce her.” Al-Hakim reported it in al-Mustadrak and said: “This is a hadith that is authentic according to the conditions of the two Sheikhs [Al-Bukhari and Muslim], and they did not narrate it.” Al-Dhahabi agreed with him, and al-Albani authenticated it.

As for whether the courageous woman falls under this description, etc., if she is not bad in character, then she does not fall under the description of as-Salfa', even if she is courageous.

Allah knows best.