I have cleared my Salesforce Certified Platform Developer II - Multiple Choice exam on 25 June 2023 and Today (29th Feb 2024) I completed my mandatory prerequisites superbadge for PD2 in trailhead. Am I eligible to receive a certificate?

Yes you are eligible for certificate here. Pls check your spam folder as well. Since you have complete superbadge on feb 29, So pls wait for some more days.