Almost everything in this post is wrong.
There's nothing to suggest the Borg "stopped" or "went out of their way" to engage the fleet. The fleet was literally between the Cube and Earth. They had more than enough firepower to force the Cube out of warp and force it to engage, or they could have all just attacked it while it was at warp. Nothing to suggest that the attack on the fleet was "unnecessary", it was literally in their way, directly attacking it all the while. It wasn't just sitting there.
Um, no. The show makes it extremely clear that Picard's knowledge of Starfleet tactics and procedures was extremely important in the Borg so easily defeating the fleet. This is made clear in BOBW and "Family" and elsewhere. It's also the reason why the Enterprise was able to at least briefly confuse and get the drop on Locutus - because they specifically went against what Locutus was expecting.
You're making this up out of nothing. Picard knows zero about Sisko's mental state, he's there to give Sisko a briefing about the Bajorans and the context of Sisko's mission. That's it. Picard isn't there to "kick" Sisko in the butt. Picard's attitude (prior to Sisko's outburst) is warm and congenial. Besides, if Picard actually was aware of any depression on Sisko's part due to Jennifer's death, Picard isn't the kind of person who would think a "butt kicking" would be the appropriate response.
Terrible theorizing all around.
One actually wonders whether Picard in fact did have a choice. Stopping to fight Starfleet makes no sense for the Borg: they could just fly right past or through the silly blockade, and concentrate on having the fight at their destination, Earth. But Picard as Locutus may have had influence within the Collective, and lured them into thinking that fighting and assimilating the fleet at Wolf 359 would be a good idea - when in fact it was but a ruse to buy time for the heroes to discover an antidote to the Borg. Likewise, stopping again and again to sightsee various attractions in the Sol system could be a Locutus move, costing thousands of lives but ultimately saving billions.
There's nothing to suggest the Borg "stopped" or "went out of their way" to engage the fleet. The fleet was literally between the Cube and Earth. They had more than enough firepower to force the Cube out of warp and force it to engage, or they could have all just attacked it while it was at warp. Nothing to suggest that the attack on the fleet was "unnecessary", it was literally in their way, directly attacking it all the while. It wasn't just sitting there.
The contribution of Picard to the destruction of the fleet is otherwise likely to be negligible. The ships supposedly didn't die because Picard revealed their secret passwords to the Collective, but simply because they were inferior to begin with and incapable of resisting a Borg Cube.
Um, no. The show makes it extremely clear that Picard's knowledge of Starfleet tactics and procedures was extremely important in the Borg so easily defeating the fleet. This is made clear in BOBW and "Family" and elsewhere. It's also the reason why the Enterprise was able to at least briefly confuse and get the drop on Locutus - because they specifically went against what Locutus was expecting.
In-universe, Picard only ever meets Sisko because he thinks the depressed Commander needs a kick in his lower anatomy before he can be trusted with doing the right thing at Bajor. Does he not realize Sisko is a Wolf 359 survivor? His degree of being taken aback doesn't readily tell - but it would be odd for him to have failed to learn this when he decided Sisko was in need of this talk. Surely he came to that conclusion through reading Sisko's file? (Indeed, Sisko's depression and his history with the Borg would probably be directly linked in that file.)
You're making this up out of nothing. Picard knows zero about Sisko's mental state, he's there to give Sisko a briefing about the Bajorans and the context of Sisko's mission. That's it. Picard isn't there to "kick" Sisko in the butt. Picard's attitude (prior to Sisko's outburst) is warm and congenial. Besides, if Picard actually was aware of any depression on Sisko's part due to Jennifer's death, Picard isn't the kind of person who would think a "butt kicking" would be the appropriate response.
Terrible theorizing all around.