Your butter sounds fine, yes there are particles (like dried milk) that settle to the bottom and brown. How dark you let them go is personal preference, kind of like caramelized sugar, but it sounds like you did well. I suppose the browned butter, after straining, looks a little darker than just melted butter, but I wouldn’t call it brown.
The cake looks OK, but it’s a little hard to tell from the photo. A few questions:
How does the height compare to the sidebar in TCB (2”)?
The corners appear cut off- did they not release when you unmolded the cake, or did they bake that way (i.e., air pockets in the pan)?
You can see from p12 in TCB that the crust can be somewhat brown, but color is not the most important factor when determining how done it is- it is done when the sides just begin to shrink from the pan. If you have an oven window and watch it, it will continue to rise in the center up to a certain point, then it will stop rising and the whole cake will shrink just the tiniest bit, leaving a small gap between the cake and the sides of the pan. That is the point at which to take it out.
Congrats on your first genoise!