A code-G Form 1099-R cannot have anything to do with an HSA. Code G means can only be used to report the movement of money between retirement accounts.
If money was moved from your employer plan to an HSA, it's a taxable distribution paid to you from the employer plan, reportable with code 1, 2 or 7, and a separate deductible contribution to the HSA made by you. In this case the employer plan would need to correct the code on the Form 1099-R.
An HSA Funding Distribution (HFD) is only permitted to be made from an IRA, not from an employer plan that is not an IRA. I can't imagine that the city plan is a traditional IRA, but if this was, an HSA funding distribution would be reported with code 1 (or maybe code 2) or code 7 depending on your age.
