In respect to Empire, cavalry is overplayed compared to real life. At best cavalry had a skirmish and filtering effect, trying to gather Intel and harass the enemy but it wasn't used to the same level as they were in the Napoleonic era.

However I haven't come across much about the diamond shape formation in the battlefield. Formations were often decided by the commander, on the spot, and depending on the terrain. Considering the methods of how cavalry committed the charge: moving into position slowly, starting to a trot, moving to a fast trot, and ending with a full on charge, the diamond might have been an idea but an impractical idea.

I believe you're referring to the "batailon carrè" formation/system. Napoleon was the first to use this tactic, although it was proposed in theory some years before and it is likely that Napoleon had learned of it as he was a voracious reader of history and strategy - often forgoing meals as a young officer so he could purchase books.

Anyway, the point of this maneuver was that it allowed a force to encounter an enemy on any side and rapidly orient the friendly unit's center, vanguard, flank, etc to counter the enemy.

Napoleon used it first with infantry during his conquest of Italy, most notably at Lonato at Castiglione. He was 27 at the time. This would be in about 1796 iirc. And considering this was when the strategy was first deployed (even though it was devised some 30 years), I guess you could say the timing is accurate, at least.

Source: among others, "Napoleon: A Life" by Andrew Roberts.