Looks like remnants of the old finish. Which means the sanding was not good enough. Re-sand it and do it again.

I’m not surprised they look muddy, these stains all contain white pigment. You are also trying to fight the natural wood tone of the wood which is obviously warm. You may be better off with a gel stain or paint to get the color you desire on this wood.

" and this picture represents the work after 2 coats of stain "

Adding to what Hallett said, two coats of a white based stain will also do this. Two coats of any stain is never really a good idea. Add in what GS Floor Service says about the original finish and you have this mess.

Hallett hit the nail on the head. This type of stain is going to be milky and not transparent.

It appears you might have American Cherry. It's a closed grain wood so it can be splotchy, but the issue in your picture is either from bad sanding or staining (more likely). It's not going to be walked on since it's not a floor, so areas of thin stain could be likely be selectively touched up.

You used semi-transparent. If you wanted the grain to show you should have used transparent. All you have to do is look at images of those semi transparent stains and you can clearly see they have a milky look to them.