Inspired by The previous version of my question
I noticed that in Nusach Ashkenaz, ברוך הבא is said at both a Brit as well as when the Chattan (groom) walks down the aisle toward the Chuppah.
Someone explained to me that the reason this phrase is said at a brit is to welcome the child into the "covenant" as he is about to "officially" join the Jewish nation / community.
But, why is this also said for a groom? I'm surmising (my drash, here) that later on during the brit ceremony we say a phrase:
כשם שנכנס לברית כן יכנס לתורה לחופה ולמעשים טובים
A literal translation of the above is:
"In the manner that he entered the brit, so shall he enter for Torah, for chuppah and for good deeds"
I'm curious if any notable (i.e. a rav, commentary, Gemarah, etc.) has explained the term כשם שנכנס לברית as meaning that in the way that he literally entered the brit meaning, hearing the words ברוך הבא, so too should he enter his chuppah also hearing the same words ברוך הבא?