Aside: banks are not the only possible HSA custodians.
All tax-trust account custodians (IRAs, HSA, Archer, Coverdell, and the new QSA) are required to file an appropriate type of form 5498 each year, which for HSA is 5498-SA; they are also required to provide you a copy, but if you lost touch with them and didn't give or update your current address those copies may have gotten lost.
I'm pretty sure if you get a 'wage and income transcript' it will include all 5498's, in spite of the name. The description on the webpage only lists the basic 5498 for IRAs, but Form 4506T (which you can download as PDF, print, fill and sign, and fax or mail) describes this as "Form W-2, Form 1099 series, Form 1098 series, or Form 5498 series transcript." (emphasis added) According to the website this type of transcript is available through thei online app, but the authentication for that is very strict -- NTA (the IRS ombudsperson) consistently reports only about 1/3 of people pass it. (I tried a few years ago, and failed.)
Somewhat similar for IRA: Catching up on 8606 forms for non-deductible IRA contributions