Yeah, I don't think the Celts are shopping Brown. I believe that they assumed that Brooklyn was serious about trading KD, so they made a substantial offer. When Brad got blown off (reportedly), he moved on. And, as far as we know, that's the one and only time Brown's name has been mentioned by the Celtics as being available for the right return.
There are conflicting narratives, about the Celtics either being in hot pursuit of Durant or about the Celtics just casually doing due diligence. I suspect that Brown was put on the table in a serious manner, but talks quickly ended because the Nets weren't serious sellers.
As for "does it matter"... Not very much right now, for everybody except for Jaylen. For him, the question of "did the Celtics offer me or did the Nets ask for me" may hold some importance. Ultimately, if he performs and gets his max / supermax contract, it will hopefully just be an interesting side note he can tell his grandkids. But, if the season goes sideways, maybe it turns into a grudge. It's impossible to know, but I think in most scenarios, JB can live with the fact that he was offered for an all-time great still performing like a star.