I took a hardship withdrawal from my 403b for higher education. Is that subject to a 10% penalty?

Yes. If you are younger than 59 1/2, such withdrawal from a 403(b) account will be subject to the 10% early withdrawal penalty.

For qualified higher education expenses, only early withdrawals from IRA accounts are exempted from the penalty.

Please read this TurboTax article for more information.

Unfortunately, yes.  The exception applies to withdrawals from IRAs, not qualified workplace plans.  Even though these types of plans are similar, they are covered by difference sections of the tax law and some of the rules have important differences, like this one.

https://www.irs.gov/retirement-plans/plan-participant-employee/retirement-topics-exceptions-to-tax-on-early-distributions