As for what Picard meant...
He didn't mean anything, because he doesn't exist. He cannot, therefore, be interrogated as to his intent; the words Stewart said are what they are and nothing more or less.
Except that precisely
because Picard is just a fictional character, his lines are subject to interpretation, because he can't say 'that's not what I meant.' So judging his lines solely by the context of the episode:
Chancellor, there is no starship mission more dangerous than that of first contact. We never know what we will face when we open the door on a new world, how we will be greeted, what exactly the dangers will be. Centuries ago, a disastrous contact with the Klingon Empire led to decades of war. It was decided then we would do surveillance before making contact. It was a controversial decision. I believe it prevented more problems than it created.
(Emphasis mine)
Picard says 'we' five times. In the context of the episode where he is acting as an ambassador of the Federation during first contact protocol (which he explains above), 'we' clearly means the Federation as a whole, who wants Malcor III to join them. Not just Earth, not just Vulcan.
The Federation. Granted he doesn't elaborate as to exactly
who made that disastrous contact with the Klingons which led to decades of war, but again in the context of his speech, he clearly means the Federation, since a direct result of that contact led the Federation (his final 'we') to adopt FC protocols. And the Prime Directive did not exist until after the Federation was formed, so the first contact protocols would also have to have been created after the Federation was formed.
Plus, as far as ENT goes, Earth’s first contact with a Klingon was neither disastrous, nor did it start decades of war. Nor was there a need for covert surveillance before making first contact, because everyone other than Earth already knew who the Klingons were, not to mention that they were already more technologically advanced than humans. So yeah, it’s a bit of a contradiction with what Picard states.
So while I appreciate your insights as to what you had in mind when you co-wrote the story, ultimately the story trumps authorial intent, which was why I said earlier that it doesn't really matter what the author (you) intended for that line.