Hey I'm a tea fanatic
If you're looking for a way to brew loose-leaf tea that doesn't involve a metal strainer, there are a lot of traditional clay/ceramic brewers that are a lot cheaper and easier to clean than teapots (which are also an option).
I recommend trying out a gaiwan, that sounds like it should fix your issues. I recommend gaiwan brewing for other reasons too, if you use ~5g of tea in a 50-150 mL gaiwan then it finishes brewing in less than a minute, and then you can brew the same leaves 3-5 times if they're good. Switching to a brewing style like this was a big part of what got me back into drinking lots of tea because I wasn't wasting tea by forgetting about it waiting for it to cool (brewing less at a time means that it cools much more quickly).
I do have a gaiwan!! I love it a lot. I snapped the lid lol but it's still functional!! it's easy to clean too
the picture on the right is this black tea from yunnan sourcing + some dried rose buds, and I'm SO MAD at how good it is because it's not something I can afford to buy regularly. it's like... chocolatey...
These two are my go-to for daily drinking. I've been cold brewing the jasmine and it's sooooo good
I also have a little green teapot :) like, you said, not as easy to clean but it's still a good alternative to plastic and metal!
