Pretty much most of the things you might make herbal tea out of could be added to your green or white tea. Hardy perennials would include perennial chamomile, anise hyssop, raspberry leaf, St. John's wort, rose hips, rhubarb, chrysanthemum flowers, Rose of Sharon flowers (a hardy hibiscus). I make lots of herbal tea blends that have lavender in them, but I'm not quite sure how that would be in regular tea. Might be nice in the white tea, which is delicate, especially in a mixture with the lemon balm or lemon grass. Bee balm, sage, yarrow, rosemary, marjoram are other perennial herbs I use in herbal tea blends. Some of them might be too strong flavored for your delicate teas, but you could experiment. All of them are nice things to have in your garden anyway, attractive to bees, etc.
https://www.helpfulgardener.com/forum/vi ... p?p=100328
Other things to add include orange or lemon peel (you can grate it and dry it for adding to tea), fennel, roselle.