I'm hardly an expert, but I do have some experience having been on one septic system or another for over 50 years. We used to make wine, also (yes, that is related).
You don't really have to add bacteria to a properly maintained septic system. You do that automatically by "using" the system. If there aren't enough bacteria, its because you're killing them with bleach or anti-bacterial products or caustic drain cleaners or paint or any number of things that shouldn't go down the drain.
We run our laundry water out into a flower garden, which is illegal in this county, but we do it anyway. I treat our drains about once a month with a product called "Digest Plus", made by Quest Chemical Corporation out of Houston Texas. I buy it by the case from an industrial supply company. It is composed of aerobic and anaerobic bacteria, and is designed to digest organic matter in your drains and take the odor out of garbage disposals. I use about one ounce in each drain in the house when we are not going to be using them for at least ten hours. When I leave for work is the best. It keeps the drains open and de-odorized with the added benefit of flushing bacteria down the drain.
Now, the reason wine-making is related: I learned a lot about yeast while making wine. This applies only to wine yeast, but I would think all strains are similar.
Yeast is a one-celled organism that digests sugars, from simple to complex. The byproducts are alcohol and carbon dioxide. Yeast won't digest anything but sugar and starch, so its utility in a septic system is pretty limited. Also, below about 60 degrees F, yeast goes dormant. Above about 80 degrees, and it dies. It certainly won't hurt a septic system, and may actually do a little good, but anaerobic bacteria is what does the real work in a septic system.