I don’t think any jeristiction allows untreated gray water to be surface distributed. Now being Oklahoma their are wide swatches where their is no inforcemet.
I used to work for a septic pumping outfit, thus I know a little bit about septic and gray water systems.
Ideally kitchen sinks and toilets should go to the one septic tank, and if one is using a gray water system you should have a tank for that. Reed beds and shallow distrabution lines for sub soil irrigation are ideal. These don’t have to be fancy.
know the kitchen sink and it’s grease are problems, especially with out a tank or grease trap. They plug up leach fields faster than biofilm.
another issue with older homes is schedual 20 pipe, the stuff is so thin it gets crushed.
another issue is maintaining 1/4 in 10 drop for black water and as a minimum for gray water. Don’t allow any sags or bumps.
soap, body oil and hard water also cause hardening of the arteries, so power snaking and enzyme cleaners might be in order.