I've updated my app settings to be Read, Write, and Direct Messages,
but when I go through the authentication page (not the normal OAuth
authorization page), it still tells me that the app won't be able to
access DMs after June 30th. Am I missing something or should that
message no longer appear
I think this was addressed in the A new permission level thread.
You said you were restricting this permission to the OAuth
/authorize web flow only. Will /oauth/authenticate (Sign in with
Twitter) support the new permission?
The R/W/DM permission can only be granted through the