There may be a couple things occurring here. Algae is one thing, and cyanobacteria (the green slime mentioned is this) is another. Cause of both are connected.
First, to answer your question about the problem algae...in a planted tank this is caused by an imbalance of light and nutrients. If the light--and this involves intensity, spectrum and to some extent duration, any one or more of which may be the issue--is sufficient for the needs of the plants (they vary, depending upon species) and if adequate nutrients are available to balance this for the needs of those plants but no more, then "problem" algae is non-existent. Here you changed the light, and from the subsequent post it may not be adequate for the plants' needs, or it may be too intense and nutrients are now insufficient. The balance is certainly out somewhere.
Algae is no where near as fussy over light, it can manage with almost any, but not higher plants. Aquatic plants must have red and blue light in order to drive photosynthesis. Adding green to this mix does improve plant growth, even though photosynthesis is dependent upon the red and blue primarily--and of these red is the more important. Which likely explains the Ludwigia dying--stem plants are faster growing and thus need more red, and a lot of LED light unless it is specifically intended for planted tanks is high in blue with very little red which is why the light is "cool" rather than "warm" in appearance. Ludwigia repens for example has a red tint to the leaves, and red leaf plants need even more red light because they appear red due to reflecting that colour, so it is even more critical. Kelvin is a good guide to spectrum, with a range of 5000K to 6500K being ideal. Another observation is that high blue without the red is frequently a cause of problem algae, for the reason I just explained.
Cyanobacteria is caused by organics in the presence of light. This too is about balance. Cyano often appears close to the surface light, or on the side of the tank that may be facing a window with brighter light. The organics are necessary to feed it, but organics are usually somewhat plentiful in an aquarium, depending upon the bioload and plants, etc.