"Your HSA summary" shows "tax-free employer contributions", which seems to include my own contributions via payroll, not just "employer". Is this a bug in the summary?

[BMcCalpin]

This is correct.

The IRS considers both your employer's contribution to your HSA PLUS your contribution to the HSA by means of payroll deduction to be the "employer contribution". The amount on line 9 on form 8889 should be equal to the amount on your W-2 in box 12 with a code of W.

The amount on line 2 should be equal ONLY to the amount you sent directly to the HSA (not through your employer); note that most taxpayers do not do this.

The amount in box 12 with a code of W is removed from Wages in boxes 1, 3, and 5 on your W-2 before it is printed. This is why you don't see a deduction on your return for your HSA payroll contributions - because they were never in your income in the first place.

So the HSA Summary is just using the IRS's own terminology, no matter how counter-intuitve that is.