No, that amount is not included in your Box 1 wage amount. And no, you should not enter that $400 on your tax return.
Anyone can contribute to your HSA, but you can only take a deduction for what you (and your employer) contribute. Since Well Health is outside of your employer, it is not included anywhere on your W-2.
Code W: Company contributions (including employee contributions through a cafeteria plan) to an employee's health savings account (HSA).
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