Turns out, there where a lot more than I expected.
Chat already has a method send_action. I added send_chat_action for completeness and both to User.
TL;DR: Both. Both is good.
I guess the logic was to skip the chat similarly to Message.edit_text as shortcut for Bot.edit_message_text, but the chat in send_chat_action acutally comes from the class name ChatAction … But having both doesn't hurt.
Also, one could think of adding shortcuts to ChosenInlineResult, which has an inline_message_id attribute, but IMHO that doesn't really make sense. It would only be needed, if one would edit the message right after it's posted (why, though?). In all other cases one usually has only the inline_message_id and not the CIR.
Closes #2034