We have one bathroom-the toilet more than not-will fill up with water BEFORE it drains-and when it drains it is super slow. The toilet is new, the pipes are also new (within 3 years) and we recently had the septic tank drained and all pipes to and from blown out for any clogs. When we are not flushing, if there is any other drain (ie washer or kitchen) used, the toilet bubbles like a stew. Not fun.

I am baffled as to what this could be! The process is-use the toilet, flush, the bowl fills up with water-becomes very high rising like it might overflow-then the "flushing" process stops-the back of the tank clicks like it is done with the process and the water (and other stuff) left in the bowl will drain slowly over the next 10 or so minutes-so never really leaving the bowl. We have plunged until our hands are raw-

What should our next step be?

when we are not flushing, if there is any other drain (ie washer or kitchen) used, the toilet bubbles like a stew. Not fun.
This tells me that you have a clog in your drainage system that's setting up back pressure. That's the sewer gas bubbles that you see coming out of your toilet bowl.
The solution would be;
1) to pull the toilet and snake from there.
2) to snake from the lavatory roof vent. If you do then put out enough cable to reach the base and 16 feet more.

I am baffled as to what this could be! The process is-use the toilet, flush, the bowl fills up with water-becomes very high rising like it might overflow-then the "flushing" process stops-the back of the tank clicks like it is done with the process and the water (and other stuff) left in the bowl will drain slowly over the next 10 or so minutes-so never really leaving the bowl.
You nay have two problems going. Check this out. I have one that most repair plumbers miss.. Look down at the bottom of the bowl. If there is a small hole, then that is a jet that starts the syphon action. If it's clogged the water will just swirl around and slowly go down leaving solids behind. Take your finger,(UGH! ) and run it around the inside of the opening. Over the years minerals build up and cut down on the syphon (flush) action. If it is rough or you feel build up, take a table knife and put a bend in it to get around the curve in the bowl and chip and scrap it clear. Next take a coathanger and clear out the holes around the rim. They start the swirling action. And last, check the water level in the tank. It should be 1/2" below the top of the over flow tube. And speaking of the overflow tube, Make sure the small 1/8" tube from the ballcock to the white overflow tube is connected so it discharges in it and that it's flowing when the ballcock fills. This is what raises the water level in the bowl. For a good solid flush they all have to work together. Hope this helps and thank you for rating my reply.. Tom