If you are age 19 or older, not a full time student and your gross income in 2023 was $4,700 or more then no one can claim you as a dependent and you do Not indicate that you were a dependent on your 2023 tax return.
Being on your parents marketplace insurance does not make you a dependent.
However, if you were a Full-Time student, in January thru May or even longer, under the age of 24 at the end of the year, and did not provide more than half of your own support for the year, you could still be considered a dependent.
Ex. You are 21 years old. You graduated from college in May and moved out. Your parents paid your tuition for the year and fully supported you for the time you lived there. If their total contributions to your existence were more than 50% of your total support costs for the year and yours were not more than 50% for the year, then they can claim you as a dependent on their return. You would need to discuss with them if they are or are not.
As for the Marketplace insurance, if they do not claim you as a dependent, you will need to get a copy of the 1095-A to add to your return. Even if you claim 0% as your amounts, you will still need to add it as a shared policy.