TurboTax insists I upgrade from free because I have a health savings account, but nothing changed in my owe/refund amounts. Am I just being penalized for having an HSA?

Contributions to an HSA for the year or distributions from an HSA during the year require filing Form 8889.  The Federal Free version of TurboTax does not support filing Form 8889.  Whether reasonable or not, this is a business decision that Intuit has made.

If you have an HSA with an existing balance but made no contributions for or distributions during the year, your tax return would not include Form 8889.

[Edit: corrected to refer to Form 8889 instead of Form 8880]

No, you're not being penalized.

As dmertz suggests above, Form 8889 is required to be reported to the IRS in this situation.  And it's not available with the Free Edition.

According to the Instructions for Form 8889,

You must file Form 8889 if any of the following applies.

• You (or someone on your behalf, including your employer) made contributions for 2020 to your HSA.

• You received HSA distributions in 2020.

• You must include certain amounts in income because you failed to be an eligible individual during the testing period.

• You acquired an interest in an HSA because of the death of the account beneficiary.