Synergy has a real meaning: 1+1=3. A cigar and a whiskey. Chocolate and peanut butter. Hall and Oates. Et cetera. Unfortunately it's one of those terms like "DevOps" or "jam band" or "martini" whose true meaning has been sullied by people trying to sound cooler than they are.
On the rare occasions I've used it sincerely in meetings I've always caveated it with some variation of "the real meaning, not the BS one." This never seems to work so I've just dropped it from my verbal lexicon altogether.
I always avoid synergy and say "bigger than the sum of its parts" or "peanut butter and jelly". Simple language with less baggage.
Why would you drop it altogether? Medications and/or supplements can have synergistic effects, for example. Synergy is actually a term that is formally defined as "Effect(A + B) > Effect(A) + Effect(B)".
Synergy often means layoffs. As in, we merged two companies and now have two of every department, one of each has to go, and the remainder can do the work of both (yay synergy).
That's the right move. If a word changes its colloquial meaning, better drop it and find a new one. Happens all the time. From stuff like "agile" in a software development context (pretty meaningless at this point, can mean anything from the original definition to the systematic micro management it got to be commonly associated with), to previously neutral words that became offensive (because they were commonly used as such).
No individual holds power over connotations. Language just evolves.