https://porchdaydreamer.com/how-to-tile-over-a-marble-fireplace-surround/

the herringbone and the tile in that DIY would look great, and I think you could leave the hearth,

The marble is quite nice. I'd look for doors or a screen. There are people who do stone repair if you really can't get it clean. If you like more detail, you can find stone trim in nicer tile shops. Maybe a little carrara marble pencil molding around the firebox?

I wouldn't necessarily buy anything from houzz, but they have some nice screen examples: https://www.houzz.com/products/contemporary/fireplace-screens

Paint it black inside and add doors for sure.

I can show you how that will look if you send the appropriate images using our Free Fireplace Design Service.

Do you actully use this FP ?

There's a bit of guesswork with these mockups since there are no pictures of the room decor, but maybe this will give you an idea of some of the available options when it comes to having a fireplace screen made to hide the stains. If you post some pictures of the room so I can choose some options and finishes that may be more appropriate.

Angle Iron Metal Trim with Fireplace Painted Black. This will allow you to choose whatever type of fireplace screen you want as it hides the blemishes.

Free Standing Screen

Frame Screen with Mesh Curtains

Simple Black Doors

Elegant Glass Doors

Transitional Style Glass Doors

Modern Glass Doors with Combination Finish

Provided by: Hansen Wholesale Fireplace Design Service

If you do paint the inside firebricks with a black color, please make sure it's with a special high temperature paint.... otherwise when you make your first fire, you'll get a nasty surprise !

I recommend paint made by Rutland:

https://www.amazon.com/dp/B000Y4MSPC

Used it for many years when I painted fireplaces black for customers.

Here is a photo of our living room.

Frame with Mesh Curtains, Andirons and Tools