A lot of brands do use bags containing plastic - which probably isn't great in terms of you actually ingesting microplastic as you drink, let alone composting - but some do not. The trick is to find the brands that don't and use them. They fully compost.
Composting
Anything related to composting, vermicomposting, bokashi, etc.
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Good to know
As GreyShuck said, many (most) teabags use plastic. Not only are these not compostable, they also release upwards of 10 to 20 billion particles of microplastic while steeping in your cup, so best not to use them at all if avoidable (you can cut the tops off the top the bags and dump the contents into a stainless steel tea steeping container to not waste what you already have).
Off the top of my head, I know that Yogi brand teabags do not use plastic in their bags, so those should be compostable.
The microplastics points by both GreyShuck & you are great, I was not even thinking about microplastics & my (& female roommate’s) health, just the issue of not being able to find a way to compost them because plastic in general.
Also awesomely help point about cutting off the tops & dumping the tea into stainless steel tea steeping container, because yes, we do have one.