"Biodegradable" is a broad term, and may not mean that the product will disappear on its own in a few days. See “Would Using Biodegradable Plastics Solve the World’s Plastic Problems?” (OneSharedEarth, 2018).
The solution is to use loose tea. However, I've realised that many teas come only in tea bags!
“Is There Plastic In Your Tea?” (Moral Fibres - UK Eco Green Blog, 2017) has a summary of different brands of tea bags that do not contain plastic - Teapigs, Twinings pyramid teabags, Pukka (each teabag is individually packaged in a plastic sachet though), Tetley (only string & tag teabags used for catering), PG Tips pyramid teabags.
“Plastic-Free Tea Bags” (Clipper-teas.com, 2018) are plastic free according to their own website.
Henderson E, “13 Best Plastic Free Tea Bags to Make Your Brew Better for the Planet” The Independent (2019) has a few others to add to the list - Brew Tea Co, Hampsted Tea, We are Tea, Eteaket, Nemi, Roqberry, Good & Proper, T2.