my brother had something like that when he first started his 3 gallon betta tank. he did a little research and said it came from his new driftwood, mopani wood to be specific. told me the wood released sap while in the water which caused fungus (or other microorganisms) to grow off it and some detached and spread to his plants like that.
when we took out the wood a cleaned up the webbing, it never appeared again.
then when he boiled and soaked the wood and put it back, the webs were back lol.