Adding finish to a painted wooden table

So I have a table made and I was told that they applied a water based paint over it because I requested it to be black. The wood they used is either palochina or mahogany. As of right now, it isn’t really rough (maybe like the texture of rubber?) but I can kinda feel the grain. I want it to be really smooth because I am using it as a computer table and really bothers me since my arms are on it more than 8 hours a day.

I have no experience in woodworking but since I had this made, I did get interested. In my research I found out that the easiest way I can add a finish on the table to make it smooth is to use a lacquer spray.

The issue I am having is that I am not really sure if I should add wood filler, primer or anything before I add more finish. I also found colored lacquer spray paint and I would prefer to use those since I would like to deepen the color that has already been painted on my table but I’m not really sure if it is the same thing as what is commonly used which is the clear one.

Hope someone could help me out on this or if you have any other suggestion besides lacquer.