@summestfirst I would recommend creating a new post whenever you want to ask a question, even if your question is related to an existing post. It's easier for others to see and answer your particular question this way.
As for your question, as the others have pointed out, the mechanism of getting a tax benefit from an HSA is different from getting a tax benefit from the medical and dental expense deduction on Schedule A. That is, your statement: "If I add to the HSA balance from my after-tax checking account funds it sounds like I will get a deduction, if I itemize on my tax returns" is not accurate.
Why? Because valid HSA contributions are either removed from your Wages (Boxes 1, 3, and 5) on your W-2 (so you don't pay tax on them), or are deducted from your income "above the line" on line 25 on Schedule 1 (form 1040) (so again, you don't pay tax on them). These two possibilities exist without regard to whether you take the Standard Deduction or itemize on Schedule A.
So you always want to pass your after-tax money from your checking account through the HSA, so that you can get the tax benefit (assuming that you don't exceed your annual HSA contribution limit).
It may happen (I can't tell from your post), that you have more medical bills at the moment than you have money in the HSA. In that case, pay the excess bills with your after-tax money, then, when the money is later added to the HSA, you can contact the HSA custodian and ask to be "reimbursed" for the medical bills that you have already paid with after-tax money. The HSA custodian will send you a check for that amount. Note that it is up to you to keep the paperwork for the bills and the request for reimbursement in case of an audit.
You can ask for reimbursements for any qualified medical expense that was incurred AFTER you started your HSA (normally when you made the first contribution). Yes, this means that if you have maxed out HSA contributions for this tax year, but will make more contributions next year, then next year at some point when the money is in your HSA, you can request reimbursement for medical bills paid with after-tax dollars, even though they were incurred this year. That is, the rules on when you can reimburse medical bills with HSA funds are not the same as when you can deduct medical bills on Schedule A.
As you rightly suspect, the increased Standard Deduction has sharply reduced the usefulness of the medical and dental expense deduction on Schedule A, which, frankly, was not very useful anyway for most taxpayers. But since the HSA tax benefit (the total dollars contributed to the HSA are not subject to federal income tax, not just whatever is greater than 7.5% or 10% of your AGI) is totally independent of Schedule A, it works out to be a much better tax benefit than Schedule A ever was.
