Is it right to conclude that “boss” came from the culture of American slavery?
No. Its use pre-dates that culture - the first citation in the OED is from 1649.
“Governor” on the other hand, connotes an official of government, at least in the United States, so how did it come to be used as a term for any supervisor in British slang? Does that reflect Britain’s monarchic history?
No. According to the OED, governor in the sense boss is first attested in 1802, at which time the word was still in general use to mean “One who bears rule in an establishment, institution, society, etc.” - a sense which is now used only as an official title in a few institutions, e.g. the Bank of England. In 1802 the head of a school, almshouse, prison, factory or monastery might be described as its “governor”.