Thanks for the pictures. From the fountain I can see a lot of suspended algae. OK, possible improvements. There are several issues which in total cause the problem.
1. Decomposing plant material, dead bodies, frog spawn.
2. Suspended algae, whether single cell (green pond) or slime (floating).
3. It's spring. Decomposition slows in winter and when water warms up bacteria go into over drive. The whitish grayish hue is probably bacteria, so much that you can see the mass.
I wouldn't list runoff as a problem, but it well may be. I can't tell from the pictures. Reducing runoff risk would be a good idea however.
The UV is not working. If you haven't replaced the bulb in the past year then it's time. Turn off the UV in the mean time as it's doing nothing. Whether you want to mess with the UV is an issue. Because of the other issues a UV may not make a big difference in the short term.
Bottom line is there is just too much decomposing organic matter in the pond. This includes the potted plants. Virtually everything else you do is never going to get a head of that waste. You could buy a dozen filters.
I would remove everything from the pond and start over. Mainly because I'd want to know what was in the pond.
I would build a concrete block collar around the perimeter to stabilize the edges to stop rocks from falling in. That will also fix most/all of the runoff issue. would also cover the liner above the water line but that doesn't have anything to do with clear water. Actually I always mortar rock over the entire liner, but again, nothing to do with clear water.
When I mortar rock the bottom I also build a "planter" out of mortared rock for the lily. That helps reduce soli/media from moving out into the pond and makes cleaning easier.
I move all plants into their own separate planter. Looks like it's in the pond but isn't exactly.
Because of your type of pond I would suggest a vacuum for cleaning. A net can be used but is more difficult. Trees on your lot, lots of plants and no skimmer or bottom drain system means vacuum is your best choice. You'd want to vacuum 2-4 times per month.
Once the "new" pond is done I'd make sure the UV was working.
Things that can help. Google "Trickle Tower pond filter". This can be as simple as a pile of rocks that you run water over. Like where your fountain is you could extend that to about 2-3' and just pile rocks around it. TT filters are self cleaning, self washing. They can get macroalgae to grow and that can kill green water algae (theory). A TT is not a guarantee for clear water and are normally considered only a bio filter, meaning converting ammonia, which you don't need. But a TT is based on a stream, it's like building a stream. We don't know how but in many cases streams seem to create clear water. I believe it has to do with macroalgae, but that doesn't matter.
Or adding a stream but I assume that's more than you'd want to do.
There is a possibility the TT only could get you the water you want. But cleaning out the pond and separating the plants increase the odds. A pond can have a lot of decomposing waste and still be clear. It's more of a question of how fresh the organic material is, how fast it is coming into the pond. There's more than one way to approach the issues.
As a general guideline a pond like yours has to be cleaned manually. Aquascape for example requires their ponds to be emptied and cleaned at least once a year. However vacuuming is another way as long as the bottom allows vacuuming. Loose rocks, plant pots, etc., can make vacuuming impossible. Which is why Aquascape requires their ponds to be emptied, they have loose rocks.
Keep up the vacuuming and get the UV working and you'll have clear water.
Buy a combo filter...prepare for more learning.
AlaPAMA
