I don't feel like tea has much affect on soap, other than it's fun to play with ingredients. You can easily replace your water with tea. The first time I did it, I used a very strong brew and it lightly colored my soap, though I haven't been able to duplicate that result. It will not scent the soap.
I have been wondering, though, about infusing an oil with mate. I wonder how well that green color would hold up.
The tea is made from Yerba mate, a shrub/tree in the holly family, genus Ilex. If you want to try using it for color, you could try making an oil infusion with the dry tea, perhaps grinding it to a powder first. The main plant pigment will be chlorophyll, which is a finicky colorant in soap and tends to fade pretty quickly. If you search for matcha, moringa, alfalfa, wheatgrass, etc. you will find a number of recent threads on how oil infusions and green plant powders behave in soap.