No, you don't have to be the primary policyholder, but be aware that you are not eligible to contribute to an HSA if your parents can claim you as a dependent on their tax return (whether or not they actually claim you). As far as I know, if you are an eligible individual and are covered by a family HDHP plan, your contribution limit is the family limit, not the self-only limit, independent of anything your parents contribute to HSAs. (This loophole was introduced when the law was changed to allow adult children up to age 26 to be on their parents' insurance policy even though they are not claimable as dependents.)
Given only the income and deductions you mentioned, I see about a $760 tax savings for a $3,450 HSA contribution (twice that for a $6,900 family-limit contribution). However, the main benefit under your circumstances is the long-term tax-free growth, not the immediate tax savings. (This also makes me question your IRA and 401(k) contributions being all to traditional rather than at least some to Roth accounts. Contributions to traditional accounts are only tax deferred, and when distributed, are subject to ordinary income tax regardless of the type of investments held in these accounts. I might be inclined to make at least the IRA contribution to a Roth IRA which allows you tax- and penalty-free access to your original contributions at any time, and tax-free growth provided requirements are met.)
