Do I have to give the new owner access to my personal email if I used it for work?

No, not simply because the business was sold — using your own personal email for work was a choice, often one of convenience, rather than a legal obligation, and a new owner doesn't automatically inherit a right to access an account that was never actually the business's own property or system.

If work-related information genuinely exists in that personal account — client emails, business records, files you were using for your job — the new owner has a legitimate interest in getting copies of the actual business content for continuity purposes, and it's reasonable for them to ask you to forward, transfer, or provide copies of specifically work-related material. That's different from being asked to hand over ongoing, unrestricted access to a personal account that also holds your own private correspondence.

Going forward, it's a sensible moment to separate the two — start using a proper work email address the new owner provides, rather than continuing to blend personal and work communication through your own account, which protects both your privacy and the business's own records. If you're pressured to hand over your personal account's full access rather than specific work content, push back on that directly.