How did 'how' + 'ever' = 'however' ⟹ 'but'?

[ OED: ] Etymology: < how adv. + ever adv. 8e.

3. Qualifying a sentence or clause as a whole: For all that, nevertheless, notwithstanding; yet; = but at the beginning of the sentence.

[ever adv. 8e. :] Appended to relative pronouns or advbs., and giving to them a generalized or indefinite force; = Latin -cumque. These combinations are now always written as single words: see howsoever adv., whosoever pron., etc.

How did the Compounding of the adverbs 'how' and 'ever' (into 'however') imply or produce meaning 3 above for 'however'? I ask not about the other meanings of 'however' here.

OED specified the pertinent definition (among the many) for 'ever' , but unhelpfully not for 'how'.

You have quoted only part of the OED's etymology for however; in addition to the main body of the etymology, it also has an "etymological note". The full etymology is:

Etymology:  < _^HOWadv. + _^EVERadv. 8e.
_{In senses 2, 3, however is the relic of an original subordinate clause (like those of sense 1), such as ‘however this may be’.}

In other words, senses 2 and 3 don't come from how and -ever directly; rather, they are shortened forms of expressions like "however this may be", with the "this may be" part being left implicit.