The very definition of "professional" is someone who makes money for what they do. So I'd say very few active pro players are poor. The number of retired players who you might consider being poor would be about the same as any other profession.
what percentage of professional chess players are poor?

It's a fun game but it's pretty played out now that no human can even make a draw with top machines.
This was the argument from 1997 when Deep Blue beat Kasparov. Twenty-seven years later and the game is even more popular because of sites like chess.com and being able to learn the game at any time with computers.
The exact opposite of what you say has been true for so long it's pretty funny hearing someone say it today.
There are 21,142 titled players in the world, let us assume they are (semi)-professional.
There are 35 grandmasters of 2700+, they can live well from chess.
That means 99.8% of professional players are poor,
or poor to be when they get older and weaker and have no pension plan.
Look at someone as strong as Danny Naroditsky. He's a 2619 player but his "career" in chess is teaching and writing. I speak regularly to a USCF Life Master who knows a large number of GMs and he said that players stuck in the 2600s eventually take alternate careers. Personally, I don't know how anyone can even call playing a game a "career". To me it's a wasted life just like Morphy said it was. Young people should focus on skills with utility and a decent paycheck and not obsess about their chess prowess.
Even 2600 players aren't close to being able to make a living on tournament prizes. Chess is living on borrowed time with the rise of the machines. I mean look at the history of chess: Kramnik retired at 42. same with Kasparov, Fischer grew to hate the game, Morphy grew to hate the game, Magnus is probably a few years away from resigning from classical chess altogether, and the percentage of players with social deficits has to be way, way, way above the norm for average people. It's a fun game but it's pretty played out now that no human can even make a draw with top machines.