meaning - Does have “well drunk” mean “to be drunk”?

Does have well drunk mean a guy who is alcoholically intoxicated?

And saith unto him, Every man at the beginning doth set forth good wine; and when men have well drunk, then that which is worse: but thou hast kept the good wine until now.

Most English translation of John 2:10 say that people have drunk adequately, have well drunk, have had too much to drink and so on.

However, on SE Biblical Hermeneutics some users suggest that the real meaning is intoxicated by alcohol.

Neither English, nor Greek is my native language, so I have a hard time understanding why the Bible translations do not translate that correctly. One possible explanation could be that have drunk adequately; have well drunk, and have too much to drink mean ‘intoxicated’. It is unlikely.