Is it true that those who spend extravagantly are actually broke?

In general, yes.

the infographic is explaining types of people use money to buy what type of products.

It depends, because they might buy some good quality pieces which last longer as well.

How people dress on the outside is not directly related to how wealthy he/she is.
But
Wealth does determine the upper limit of what he/she dresses in. If your friend is dressed in luxury items and in different styles every day, he/she is probably really rich.

The notion that individuals who spend extravagantly are actually financially broke is a common perception, but spending habits and financial stability can vary significantly among individuals. I dont think there is a real trend towards either side of this idea or I have not come across any data that suggests so.