Rishi Simple Brew

Baking soda, hydrogen peroxide and hot water make a good mix to soak metal teaware in.
You could start with a table spoon of baking soda, an ounce of peroxide and 8 oz of boiling water and soak for half an hour.

I have been using Mandala Tea’s Smart Soak Tea Stain Dissolved for years. Love this stuff. It makes my metal fine mesh tea baskets look like they are brand new in about 15 minutes. It’s good on stained ceramic tea ware, too. https://www.mandalatea.com/teaware/smart-soak-tea-stain-dissolver

I put my French Press in the dishwasher every so often and it cleans the stainless part well.

I also second White Antlers, Mandala’s Smart Soak is amazing for deep cleaning teaware. :)

Denture cleaning tablets work really well for removing tea stains from glass and porcelain.