Yes, that's correct! In this sentence, "to be done" means "to have finished" or "to have completed" something. So, the sentence means: "I'm glad I have finished my project."

Grammatically, it is an adverbial phrase that modifies the adjective "glad" to explain *WHY* you are glad. You are glad because you are done. Infinitives can act as adverbs, nouns, or adjectives. Here are examples: "To be done with my project is something I am glad about." (noun) "That is the project to be done by us." (adjective. It means we need to do that project.)

Correct! That’s exactly what it means. To be done with something means you brought something to completion. Have a nice day 😎