As stated in the title, I am in doubt between using "I want to thank" and "I would like to thank" to expresse acknowledgment for the supervisors and the committee members in a thesis. I have used "I would like" at first, but when I checked it using Grammarly, It proposed to be changed to "I want to as": The phrase I would like may sound unconfident. Consider removing it or changing it to more direct language.
What is the more appropriate expression to use in this context?
Both are acceptable. "I would like to thank" is slightly more polite, because it is a kind of "indirect" speech.
Grammarly flags this because (I assume) it is built on a particular style guide that emphasizes direct speech patterns. With expository writing, qualifications might sound "weak". For example:
I think it may be true that the African Elephant is larger than the Asian Elephant.
Instead you should know whether or not it is true, and say so with confidence:
The African Elephant is larger than the Asian Elephant.
However confident, direct speech is not always the best option in every situation, especially when expressing humility and gratitude.
I would like to thank my parents, without whom I wouldn't be.
