You use your obi to hold the fukusa cloth, but you can also carry your car keys in the same way!
It is not a requirement to wear kimono in order to do tea, but tea is adapted to a bunch of details of kimono that make some aspects of tea much easier to do when you *are* in kimono. Some people wonder about the status of kimono as a form of national or traditional dress: the word kimono just literally means “thing to wear” or “wearing thing”-- it’s like “clothing” or “garment” in English, but of course there are lots of different kinds of wafuku, meaning “Japanese clothing” even though the majority of Japanese people in Japan today don’t wear wafuku that often, and many don’t know how to get dressed in kimono by themselves, but rather go to professional studios to rent kimono or be styled for special occasions when they want to wear it. You can also go to rental studios for tourist purposes in Kyoto and other destinations, an activity that is popular with both domestic and international tourists.
So, how might you not know how to wear traditional clothing? The main reason is because the traditional clothes of Japan were designed to be very flexible– rather than being tailored and sewn to fit individual bodies (like western clothes evolved to be), kimono are wrapped and tied and sewn to fit different folks in different ways. In preindustrial societies when fabrics were a very big expense, this is kind of a genius way to make fabric clothing for useful, since lots of people of all different sizes and ages could lightly alter and tie kimono to fit them well. Your kimono can also sort of accommodate the way a body changes from month to month or year to year (maybe even day to day!) in this way as well, since you re-fit it to you every time you put it on.
Over the last few decades, kimono dressing has become more and more formal as dressing in wafuku became more of a special occasion thing rather than quotidian clothing. (This happened much earlier for men’s clothes– more like a hundred years ago, which is why it’s harder to find men’s wafuku in flea markets and secondhand stores.) Today, there are sometimes divides between folks who have learned kimono-dressing from the established schools that teach you orthodox ways of doing it (you can get a certificate as a dresser or even a teacher of dressing!) and those folks who are still wearing kimono for everyday or working purposes – not only tea people, but also folks who work in certain traditional restaurants and inns and a few other places. For Tea, we try to split the difference between looking good and formal (it is sometimes a special occasion type thing) and being able to run around working: building fires, cleaning and setting up rooms, and making, serving, and sharing meals, sweets, and tea. I find that the best education in kimono is help from folks who wear it a lot and then practicing until you know your own garments and body well. And then the wide world of creative new takes, formal wear, and specialty outfits starts to open up to you!