But it appears from dictionary definitions and examples that diverse is only used to describe a group or groups of people as different from each other or data being different.
That's not an accurate interpretation of the word (or its definition).
From Merriam-Webster's definition of diverse:
1 : differing from one another : UNLIKE
// people with diverse interests
2 : composed of distinct or unlike elements or qualities
// a diverse population
Diverse is an adjective and it's used to describe any number of things that are different from each other. It can be people or data, but it can be many other things too.
As in the definition of its first sense, you can have diverse interests (as it's used in the dictionary's example sentence), diverse food, diverse schools. Or, as in your case, diverse experiences.
If you use the singular, it needs to be something that contains other things. (In the dictionary definition, a diverse population contains many different people.)
So, you can't say that you have a diverse experience because that's a single thing that doesn't contain anything else.
But you can say that you have diverse experiences because each experience is different from the others.
So, either of these is fine:
You have diverse experiences.
You have a diverse professional history.