I understand now. I'd forget about testing the water. I mean you can, but then what are you going to do with the results? In a pond that size, mud bottom, it kind of is what it is. There are things you can do to support more fish, which would lead to more fish, which requires more support, which...you get the idea.
Looks like a lot of fish. Normally many die but you wouldn't notice. Personally I'd want the heron there. As Dr Eric days, either you cull fish or nature will do it for you.
The fish are swimming into the incoming water just because they want to see if the grass is greener on the one side. That's their nature. There's no reason to think there's more O2 in the water coming from the smaller pond, at least no reason I can see based on little info. Low O2 and they'd be at the surface everywhere. Plus this time of year the water's pretty cool, which holds more O2. Later there will be warmer water, less O2, and more organic decay, less O2. If O2 is a problem that when it will happen. There are aerators for that size pond, but pretty expensive to run. Again, we're back to allowing a larger fish load and getting a larger fish load.
I'd sit back and enjoy. Let nature take care of it for you.