Not all employers offer HSAs to go along with their HDHPs. Mine doesn’t and it’s very frustrating. I want to save pretax money in an HSA but I can’t.
In fact once you have enough money in there that you are moving out of liquid investments then you definitely want to shop around for HSA much like you would for an investment account.
(FWIW, I have an HDHP, employer HSA, and an individual HSA that I roll my employer funds to annually for lower-fee investing.)
https://www.oldnational.com/thehsaauthority
And for comparison, https://thehsareportcard.com/hsa-authority / https://thehsareportcard.com/the-top-10-investor-hsas-1 . The landscape may have shifted since the last time I did my research.
If you have your HSA contributions made through your company's payroll department, then you don't have to pay FICA taxes on it.