The way you use that leverage is then explain why you feel something is not fair. In a professional context, you can explain your position in legal terms when you take a compassionate, kind stance, smile and analytically explain the situation from both sides.

It's no more different than handling a code review.

Now, two things can happen: Either your employer is amazed that you both created a new product AND can navigate business negotiations. This is good for your career (unless your employer is an idiot).

Note that creating a new product that people love increases your market worth tremendously (unless you are already at a fairly well compensated level).

Traditionally the simplest way to compensate employees has been to give them a raise. Hint - you could ask this :)

The funny thing a higher pay grade does is that suddenly management will respect you more (we pay him x dollars so he must be awesome).

Or, the second case: you find out your employers 'mr. Niceguy' culture is actually a charade to fool people working at below market rates. At which point the fate of your sideproject totally depends on the legal feedback you received. And it would be better for you to find a better employer.

There are really good books on negotiation and influence. I suggest you read them when you have the time. Examples: Cialdini, 'Influence'. Voss, 'Never split the difference'.