I m on bench for the past 3 months, got an appraisal score that needs performance improvement, and HR asked me to resign

My honest suggestion, if it's coming from HR, it doesn't means only that HR has targeted u. It means company decided based on your performance metrics. An HR never takes a decision on their own. They themselves are puppets.
I'm sure on your bench, u must have upskilled on one or other technology, build a good resume with big exaggerated context. Start applying to companies and tell HT sure, but I will want to serve full notice period as this is sudden for me. Convince them both professionally and if not agreed, emotionally.

Finally in your notice period grab a better offer, write a thank you mail for HR and say bye bye.

My sincere suggestion - it's better to struggle in new place rather than being stuck at an old place.

Think about it calmly cuz it's your final call

Don't resign, contact some high level official like DU lead or leadership person and tell your situation they will somehow put you in some project.