No offense intended, just trying to help.
I culture tetraselmis, have a microscope and centrifuge. I have concentrated tetraselmis to millions of cells/ml, beyond any natural level, and it still doesn't look like that pic. Live tetraselmis is always a bright green color.
But regardless, without a microscope ID I'm not sure. Maybe the color representation in the picture was off? But I have seen multiple cultures transform due to contamination. On more than one occasion, my nanno cultures have changed into tetraselmis due to contamination. The only way I found out was by putting it under a microscope. You cannot tell the difference by eye, just looks like green water. Cyano is a wild guess, but it's the right color, clumps up at high concentrations as you described, and is a very common phyto contaminant. I would not expect you have only cyano in your culture, but frankly kinda doubt it's just tetraselmis either. Especially if you never checked it for a year in continuous culture.
And like anything you cannot increase light intensity indefinitely. Any photosynthetic organism will die if given too much light.
I don't know the max light intensity but I've found above 500 PAR tetraselmis starts to bleach. Nanno, Iso, and everything else I tried completely died at that PAR level and so I had to switch to less intense lighting.
My favorite references for hobby culturing are below:
We'll survey useful types of phytoplankton, discuss why they are important in our home fish breeding efforts, and examine what it takes for home culture of these microalgae.
reefs.com