That is some classic hair algae. Its quite difficult to balance out and remove naturally. I don't agree that it would be high phosphate, that tends to be a myth but it is a good way of selling phosphate pads. There is a lot of evidence out there that show that excess nutrients do not cause algae. It is much more likely that it is an imbalance of CO2 and light is the cause or a nutrient deficiency which is slowing plant growth. Algae also excels where CO2 levels vary a lot, plants not so much.
I would either use a dosing pump if your going liquid if you can't do it daily (ideally before the lights come on) or just not bother.
On a planted tank light ideally needs to be your limiting factor, but in a low tech tank it tends to be CO2. You want to cut the light down to try and find balance, but its really trial and error every tank is different.
There are a few things that eat it but other than amano shrimp I wouldn't recommend any for your tank. I'm surprised that you have issues with them and a betta, they tend to get as big as one.
The easiest way to manage it is manual removal and targeted liquid co2 using a syringe/pipette, its really good at killing algae with direct contact, most plants don't seem to mind. Turn off the filter for a few mins while you do it and then turn it back on doing it at a water change is more than fine. I do have liquid CO2 but only use it for this reason.