Update: It's grown back and is multiplying fast. Did more research and I believe it isn't fungus (I've no fish in the tank) or algae (took some samples out and it wasn't green at all - just milky white) but probably bacteria from too much Ammonia (2ppm) / New Tank Syndrome. Reports seem to indicate it being harmless but I took it out with a turkey baster just in case.
Hope this helps anyone coming across "milky / cotton / snot / spiderweb stuff in new (uncycled/cycling) planted tank", I'll keep this thread updated if something more happens!