I looked into this a few years ago and what I found suggested that the tied or stapled bags should be fine. It’s the crimped edges bags you want to watch out for; plastic particles in the paper are how the edges are fused.

Whatever evil fuck decided to integrate plastic into something they knew was going into boiling water to save .001 cents per bag should be blasted straight into the sun.

You can avoid all of this and buy loose leaf tea instead.

The study tested bags that were made out of nylon-6 and polypropalene. You should be able to check with your tea brand and see what they use. The brand I drink at home says their bags are 100% cellulose… which is, at least, a polymer also present naturally in the tea itself.