When making hot tea, the water temps can kill the bulk of the bacteria, so fresh leaves are no big deal.
With sun tea, using fresh leaves can be a bit of a risk, since bacteria on the plant's surface can quickly populate the warm water.
So, you may want to do something to thoroughly clean the leaves, first.
Soap and water, or a scrub with lemon juice & salt, or a soak in vinegar followed by thorough rinsing in clean water.
Then muddling the leaves & using in tea. Adding citrus juice into the water may also help bump the acidity to reduce bacterial growth.
o_o I have had more than one sun tea jar get cloudy & slimy from improperly washed leaves and forgetting to drink it fast
enough, so tbh I tend to do cold-steeped or 'instant' tea instead.
I prefer to crush fresh mint leaves thoroughly in the mortar along with a little sugar, rinse it into a glass, and drink it like that - make it per-glass, or just enough for a couple glasses I'll drink that day, instead of making a bunch that I'll drink later.
Regarding mullein in particular, I don't think there's anything to worry about with the leaves?
Don't eat the seeds.... but other than that, you
should be fine.