You’re ironically perpetuating a myth that cast iron needs special care. You can clean cast iron with soap just like anything else. You just have to make sure it isn’t wet for extended periods of time

Oh you can drink the powder? You don’t need to remove it?

Nope. Matcha is meant to be ground fine enough such that it suspends in your liquid and is drinkable without filtering.

Is there a tea like matcha that would be good to cold brew?

Sencha or any other green tea can be cold brewed. I’ve never done it myself, but pretty sure you just throw tea in some water and let it sit for a while. I’ve never done it myself, so just look up “cold brew green tea.” Granted, this will only be like matcha in flavor and not in mouthfeel. Furthermore, if you plan on adding milk, this is probably not the best route to take since green tea is generally much weaker than matcha, so adding milk eliminates any semblance of flavor from the tea.

It’s that simple

Yep

By immediately you don’t mean in one go right? Like I can drink it in like 2 hours right?

The matcha will settle out if you let it sit. However, you can just shake it up again and then drink it after letting it sit.

Matcha is traditionally made with water. Using milk, like in a matcha latte, is a newer trend. Look up a traditional match recipe using a whisk. Note, I know that most people do this with ceremonial grade matcha, but I’m not sure if people do this with lower grade matcha (for example, the bag you might buy at Costco). It sounds like you are probably not using ceremonial grade, so I can’t vouch for how good it will taste. However it’s still worth experimenting with.

“Cold brew” matcha doesn’t really make sense. The goal of cold brew is to extract flavor from coffee/tea leaves over a long period of time using room temp/cold water. However matcha isn’t really meant to be extracted, it’s meant to be suspended in a liquid and drunk. If you want a “cold matcha drink” rather than specifically cold brew, I would try just throwing some matcha with some cold water in a mason jar, pop the lid on, and shake it up. Then just drink immediately.