Is the Ethiopian word "falash[a]" related to the words Philistine or Palestine?

I apologize I don’t know how to read Amharic or Ge’ez well (at all) [I am most certainly only an amateur at linguistics], and my Hebrew and Arabic are also poor. But I can’t help but wonder if the the South Semitic/Ethiopic words "falasha" and/ or "falash [mura]" share the same triliteral root P[h]|L|S, as
ف|ل|س/ or פ|ל|ש derive the words Palestine, Philistine, etc.

I ask because most sources today (for instance, the Wikipedia page on Beta Israel says:

The derogatory term Falasha, which means ‘landless’, ‘wanderers’, was given to the community in the 15th century by the Emperor Yeshaq I, and today its use is avoided because its meaning is offensive. Zagwe, referring to the Agaw people of the Zagwe dynasty, among the original inhabitants of northwest Ethiopia, is considered derogatory, since it incorrectly associates the community with the largely pagan Agaw.

However, the Agaw people clearly included some Jewry at this time; and it seems far more likely it originates from shared triliteral root rather than, for example, the suggested relation (under Texts, on the same Beta Israel page) of "Fālasfā" to the Indo-European derived "philosophy (by way of "sophos").

I have no doubt that in one place or another, perhaps many places, the term is or was derogatory. But the text I cite above has no citation for "falasha" meaning "landless", etc., and the rest of the paragraph is in passive voice, rendering it unclear where or when "its use is avoided because its meaning is offensive".

So: is this word avoided, as such, in Israel (where most formerly Ethiopian Jews now live)? Or s it also avoided in Eritrea and Ethiopia?

Why would the a word for "landless" be offensive? I assume it is offensive in the way the "the n-word" is offensive, not in the way "the f-word" is offensive? Is it offensive across time periods, cultures, languages, and ethnicities?

Put another way, should this word be considered "offensive" in all of English, Modern Hebrew, Ancient Hebrew, Arabic, Tigre, Tigrinya, liturgical Geʽez, and Amharic?

Or is it offensive now, simply because it conflates Jews from, lets call it, "Greater Canaan", with Palestinians or Philistines?