How do I set Maximum emission strength? Is there a way to set the Maximum strength of a material using nodes?, I tried this thinking it would make any values higher than 10 to be set to 10

so, with my logic this would "work" because the maximum value possible is 10 but the value is 76.3, and because it's higher than 10, then 76.3 gets converted to 10.

but clearly I am doing something wrong because it doesn't work :/
As the name implies the Maximum operations picks the maximum of the two input values, meaning it chooses the greatest of the two.

In your case by calculating the maximum between $10$ and $76.3$ you obtain a resulting intensity value of the highest input, hence  $76.3$.

From what what you describe you seem to want the opposite operation. If you set it to Minimum it will pick the smallest value of the two, effectively limiting emission to $10$, or whichever value is lowest.