Thank you for your reply. It is a valid enquiry. I guess in older stages of Egyptian expressions like
]ꜥnḫ wḏꜢ snb or
Im htp might have been common, but there are no attestations for their use in Coptic
I would translate this as: "I am asking about you" rather than "I greet you".
According to Crum's Coptic Dictionary (1939) ϯϣⲓⲛⲓ ⲉ̀ⲣⲟⲕ means I greet you, which matches with the opening formula of multiple Coptic correspondence letters. It might have a literal meaning, but, effectively the meaning is I greet you. ϯϣⲓⲛⲓ ⲙ̀ⲙⲟⲕ would be I ask you
I'd translate this as "I worship you" or "I bow down to you". We say it often in the mass prayer. "We worship you Christ with your good father and holy spirit"
ⲧⲉⲛⲟⲩⲱϣⲧ ⲙ̀ⲙⲟⲕ ⲱ ⲡⲭ︦ⲥ︦ ⲛⲉⲙ ⲡⲉⲕⲓⲱⲧ ⲛ̀ⲁⲅⲁⲧⲟⲥ ⲛⲉⲙ ⲡⲓⲛⲉⲛⲩⲙⲁ ⲉⲑⲟⲩⲁⲃ
According to Crum's Coptic Dictionary (1939) ⲟⲩⲱϣⲧ means greet, or worship
I know ⲟⲩϫⲁⲓ means bye but I did not know it could also be used as greeting.
This was according to ⲡⲓϩⲩⲅⲟⲩⲙⲉⲛⲟⲥ ϣⲉⲛⲟⲩⲧⲉ ⲓⲥⲁⲁⲕ in Copto-Arabica curriculum, I have not come across this as an initial greeting, however, in some cultures, greetings/bye are one word.
I just feel like surely Egyptians greeted each others prior to Christianity. How come we don't know any general greeting that is not rooted in Christianity.
Most of these greetings except for the Pauline greeting are not Christian, they have been used by non-Christians in correspondence. Greek loanwords predated Christianity by centuries. Alexander the Great conquered Egypt in 332 BCE. At that time, Coptic was virtually non-existent. Demotic was more prevalent. By the time Christianity enters Egypt Coptic as a linguistic stage was still developing. Some historians, argue that as Demotic (as a script) was fading out, and Coptic was still developing, there was a small stage of collective agraphia, where people spoke Egyptian, but wrote mainly in Greek because Egyptian scripts were not known to the masses.
By the time, Coptic was a mature stage/phase of the language and outgrew Old Coptic, the Hellenistic civilisation was dominant in the old world, and many Greek loanwords, became part of the vernacular, not the elites, just anyone using Coptic language. It would possibly sound unusual for a Copt at that time to differentiate between words based on their etymology whether they came from Demotic or Greek. Hence, constructs like ⲕⲁⲗⲱⲥ ⲁⲧⲉⲧⲉⲛⲓ̇ or ⲭⲉⲣⲉ ⲛⲁⲕ, ⲧϩⲓⲣⲏⲛⲏ ⲛⲁⲕ feature Greek loanwords within a Coptic phrase that abides by Coptic grammar and Greek loanwords are fossilised in a certain structure usually nominative state (Greek endings tend to vary depending on whether the word was a nominative, accusative, genitive, dative, etc.), this does not happen in Greek loanwords, they get fossilised and treated like a Coptic word.
For example, in Egyptian Arabic there are multiple loanwords eg Alo, hi, hello, bye bye, OK, tamam, effendim, agzakhana, oda, shanta, baltagy, balta, police, serenga, antibiotic, mobile, merci, fatura, balcona, vizita, veranda, salon, latte, cappuccino, shai, tarabeza, gollash, macarona, barlaman, logha, dostoor, qanun etc. These are all loanwords, that entered both Egyptian Arabic and some entered classical Arabic. One might want to try to explore Egyptian Arabic before Ottoman/Turkish, French, English, Italian influences, but then, one is bound to go back in history 600 years or so.
More or less, it is likely that a situation like this existed in Coptic, these terms (with Greek loanwords) seem to have been used since the dawn of Coptic as we know it. If one wants to explore Egyptian language before any Greek loanwords, then that would be ultimately before Coptic language itself, possibly Demotic would be a better candidate.
Otherwise, Greek (loanwords, expressions, rhetorical style, alphabet) are part of the package and parcel of Coptic language (part of the DNA of Coptic language if you may).