It’s pro sports. When you say its prestige is declining because the sport’s popularity is declining, you’re being redundant; popularity is prestige in pro sports.
Boxing just isn’t the sport it used to be. There’s a variety of reasons for this, but to point something out about your specific question, let me ask you this; WHO is the world heavyweight champion? For it to be a big deal, you need to actually be able to identify who that is.
However, you can’t. Right now there are four champions; Anthony Joshua (WBA, IBF, and WBO) Deontay Wilder (WBC) and Manuel Charr and Trevor Bryan who, to my confusion, are also listed as champions by the WBA. And that’s actually a reasonably simple picture by the standards of recent history.
There have been different boxing federations for a long time, but historically there was always a concerted effort to have the heavyweight champion be one person. Had you asked who the champ was in 1953, 1975 or 1989, the answers were, respectively, Rocky Marciano, Muhammad Ali, and Mike Tyson, with no serious dispute. Not everyone always agreed, but they usually did. That started to fall apart in the 1980s; the IBF started announcing its own champions in 1983, the WBO in 1989, and it’s hard to care about a championship where no one agrees on who the champion is. It would be like if four different teams won the Super Bowl every February.