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You might need two more support legs in the back about half way between the existing corner legs.
You will want to also have bracing in the joint. I would do something bigger than your little square. I diagramed two options. Red or Green. You can wood or plate steel for this.
My current desk is basically this set up. so in general yes where you have the legs is where you will need them.
Where you have your bracket however, I would make it a lot longer to help spread the torque out some more, you might even let it go all the way to the back of the table and put another leg down there to help support or just move the one from the corner to line up with the front edge of the other table on the back, as you correctly guessed where you have the blue bracket mark is going to be the weakest spot.
I hope my description was clear enough.