You can tone it down with a semi-transparent color coating. Look up Romabio paints.

I plastered mine

Paint it a solid colour. It sure is homely LOL.

You could fill in the grooves with mortar and do a mortar wash. or an ”over grout.” Emily Henderson and Chris Loves Julia both have the process on their blogs (chrislovesjulia for the DIYer).

We have the exact same stone. It holds dust and always looks dirty. When you go to remove it, it will likely pull off all the drywall behind it. Removing it is not in our budget, either. It sucked up all the light in the room. I tried whitewashing it, but the brown still showed through after multiple coats. I know you don't want to paint it white, it you might want to consider a different color. One of the problems with ours was that many of the rocks also had lava-like holes in them. I ended up squishing some silicone caulk into them so we did end up with a bunch of polka-dot-looking spots. We ended up painting it a flat white. Whatever color you use, use a flat paint. Makes it more muted.

Seeing as you are doing your flooring now, I guess you won't remove the hearth to minimize the FP in the future.
Eventually I would take the stone out and reface with tile or wood or drywall. Maybe get a gas insert. Seeing as it might be in 3-5 years, your color taste or wishes might change, but overall when you do it do it properly and take the stone out and make it the FP you want, not just a band-aid of painting.

Before all of that though, I would take off the chair (?) rail molding as it seems too high and cuts the wall height oddly.

We are keeping extra flooring in case we change the footprint (it’s LVP, so easy to replace planks) - I like the fireplace, just hate the stone. I like the idea of changing it to gas.

As for the chair rail - this room is a lower level (not basement level) in a trilevel home, so that’s actually part of the structure of the house. I think I’m going to do a board and batten on the lower and wallpaper the upper to kinda hide it, bc I do agree it’s at kind of an awkward level.

Also this is updated photo with paint.

It looks better with this color of the wall - it’s a bit of a warmer white IRL, but not creamy.

Replace the gold end irons and screen that will help it not look dated

Honestly, a houzzer just posted this on another thread; for your fp room, I thought it 'cool', updating enough to post here, hope that's ok:

https://www.rugs-direct.com/Details/LioraManne-Marina-TribalStripe/140280/225894

I would agree the brass is dating and keeping it in the 70s. You will be amazed at the face lift a new front glass/screen will give. It's a stone fireplace leave it be! It is ok for it to be what is was built as.

Is this your living room ? Family room ? Entry room ? If this is your living room I would rip out the window and put in a large window to get more light into the room , perhaps even a sliding door with a terrace to make your room look larger and brighter . To me the fireplace looks nice ..perhaps re grout and use a little of the grout to wash o er the stones . I have a similar fireplace ...I like it .