If a labor contract is not signed, the employee shall go through the formalities of resignation. It will not be blacklisted, and it will not affect the job search in the future.

Because only if you sign a labor contract and violate the relevant terms in the contract will you be punished (including blacklisting) according to these terms. Moreover, even if there is a labor contract, there is no problem in fulfilling the resignation procedures in accordance with the labor law. So, don't worry.