Local health department. But don't let anyone know you don't know.

Look up Septic Tank Inspectors for your area on Google. Most if not all will repair or replace them, too. They will be private companies, but they will have certifications.

The inspector that did my house inspection was qualified to inspect my septic system. Took the lid off, took care samples form the leach field, checked flow rate, etc.

In my area, it's septic system contractors.

Most companies that pump septic systems can inspect. And the seller should be paying for pumping. Buyer pays for inspection.

I had a local septic cleaning service inspect the septic system. But not the same septic cleaning service the seller used to clean the system.

If this is new construction, there is no need to inspect. It is warranted.

If this is an existing home, but new to you, it can be inspected by a local septic service. Just be certain to be present when it is inspected. You will be expected to pay for the inspection.

The owner could have already had it inspected and serviced. You still need your own inspection. If it hasn't been serviced, make it part of your offer requirements. If it has been serviced in the last year or so and there is documentation presented to reflect the servicing, you don't need to insist on a servicing, just on an inspection.