Filtering urine requires removing any ions from the solution. Methods that we use to do this are:
-reverse osmosis (hydraulic pressure forces water through a membrane)
-forward osmosis (osmotic pressure forces water through a membrane)
-biochemical reactor (what spacestations use, bulky and slow)
-nanofiltration (hydraulic pressure forces water through a membrane, only partially effective, usually uses as a pretreatment for other methods)
-thermal distillation (boiling water, heat can be provided by electricity, geothermal, or fuel for quick use and sunlight for slow use)
-vacuum distillation (boiling water by using ultralow pressure produces by an air pump)
-freeze thaw (exactly what you think it is)
-membrane distillation (utilizes a temperature gradient to move water through a membrane)
-electrodialysis (uses an electric field to move ions through a membrane)
-chemical deionization (ions stick to chemical beads which are periodically replaced)
Most of these are slow and require huge amounts of energy. If this wasn’t the case the water shortage crisis would be solved in an instant worldwide. This also of course makes them completely unpractical for backpacking. Chemical deionization does not require lots of energy but it is slow, bulky, and heavy. The same is true for biochemical reactors. Solar distillation is far too slow. That just leaves forward osmosis. This is somewhat practical for backpacking use but nobody sells such a device. The membranes are hard to produce, foul quickly if not regularly treated, require you to already have some clean water to start the reaction, and do not produce pure water. You need to add a chemical, usually sugar, to the mix to create the osmotic pressure. Also it’s sssllllooowwww. Keep in mind that you only pee out some of the water you intake. Some comes out with your poop and some is sweated out. So you’ll still lose water over time since you can only “recycle” some of it from your urine.