Is a tweet a legal authorization? I really don’t know.
No it would be followed up with official correspondence. Agencies don't respond to tweets if they want to cover their butts which they all do.
The tweet may not be but the content on the tweet matters:
"Note: he used the words I have fully authorized...
That is presuming the rest of President Trump's sentence continued:
"..release of unredacted material from the fake russian collusion investigation.."
Any legal indictment that would result from these documents would come from the DOJ, and they already HAVE them.
Therefore, any declassification and release is for the publics benefit - for political purposes.
Presidents tweet was to make a political point: namely, that the information, if released, would be damaging to the Democrats. By saying he authorizes it - he signals that hes not bluffing..
He is announcing weeks before the election that he is holding all the cards...