My multi-tank "filter" is now working, though it still needs some work.
At the moment there's not much to it as far as a filter goes other than some activated carbon. So it's more of a water circulator.
Rather than also have a bottle inside the tank, it occurred to me that the siphon tube can just go straight in as long as the contraption on the outside is as high as I want the water level. It could handle higher water flows with the internal bottle but presently the fill tube is aquarium air hose, so there's only about 7 gallons per hour going into the tank.
This part doesn't seem to leak anymore. I printed it out of ABS plastic which I usually don't use because it's harder to work with, though in printing it I noticed an expected problem and was like "but that's just because it's not cooling fast enough." So I turned on the fan and the problem went away. So maybe ABS isn't that bad and I just didn't know how to get good prints before. It was the first kind of plastic I ever 3D printed with. A second one I printed, for which I had the fan on the whole time, came out better than the one I printed with PLA.
Anyway, I printed it in ABS because ABS can be momentarily dipped into acetone, which will melt all of the individual layers together to make something more solid and water-tight. I then applied more acetone before screwing it onto the bottle. I don't know if that made a difference, in particular the PET plastic of the bottle doesn't seem to be affected by acetone so I don't think it fused them together, but it doesn't seem to leak anymore. The output hose is simply held into place by friction, being squeezed into a hole that's a bit too small for it.
The drain hoses just go into this bucket. I hadn't anticipated that it would be important for the drain hoses to not actually go into the water. Air ends up in them and if that air has to be forced under the water then that just backs up the hoses because they're gravity-fed.
Figuring out how to attach small hoses to the pump output was one of the more difficult parts. At the hardware store they have all kinds of connectors and hoses, the most promising of which seemed to be the hoses to supply water to ice makers, but I couldn't figure out what was supposed to adapt those lines to normal plumbing, and all of the fittings I was looking at were expensive. What I ended up doing was going to Walmart and buying T connectors for airline hose, drilling holes into a CPVC pipe, and using super glue (cyanoacrylate) to glue the T fittings into the holes.
This isn't anything I want to run all the time because I'm afraid it'll leak for a number of reasons. Those friction-fit connections might come loose, the siphon hoses might get bubbles in them, or the intakes to the siphon tubes might become clogged. However, I do like the idea of this kind of system because it means that the water in the two tanks is identical and I can swap fish between them without having to give them time to acclimate to the new water. It also kind of means that water changes are easier, as I can just dump out the bucket of water and dump new water in it and I'm done. ...or it could be that easy if I didn't have to soften the water first and then adjust the pH. So I might have to see what I can do to make it more reliable.
One idea I have is to build water detectors and connect them to something that can switch off the pump if the water level in any tank gets too high or if water is detected somewhere that I anticipate leaks.