I would consult a local realtor. about 3 vs 4 bedrooms

I would ask a real estate agent or two what they think.

When we lived in Pasadena CA some years ago and housing was at a premium we switched our fourth bedroom into a family room by opening a doorway from the front bedroom to the living room—just the opposite of your idea. But we needed a family room. The house sold quickly when we were ready to move.

Posting a floor plan might help.

Personally, I’d think that filling in the door way to make the family and living rooms completely different rooms would be a plus regardless.

But with the renovation make changes so the space can still pull double duty. That way you can list with either the 4th bedroom or family room and appeal to a bigger audience.

Look into the implications of adding another bedroom with the planning office and the tax assessor to avoid surprises. In my locale, adding a bedroom to a house with 3 or fewer existing bedrooms triggers an impact fee. There has been talk about removing this fee on remodels but I haven't heard that this has actually occurred. So, remodels here add studios, media rooms, playrooms, dens, etc but not bedrooms.

Check on an appraisers forum to see if there would be any difference in value.

Unless you are getting cash for the sale or a large down payment from the buyer the appraisal will be the determining factor if you actually get more at the sale.

If you do this change, do it for yourself and not for resale.

If you do this change, make sure you don't make the current floorplan dysfunctional as that will take value away.

If you are using the exact same square footage and not adding any, then it is doubtful that your home would add value but you would need to get twin sales in the area to see how much, if anything, is added to the value. It may open up the buyer pool and sell more quickly though. As the others mentioned consulting with a couple of Realtors in your area would help you get a handle on the current market.

Would it make sense to add the closet as you are talking about, and then make the door into the living room a double door with pocket doors? That way you could leave it open most of the time for a spacious feel or two separate rooms, and if anyone wants to make it a bedroom, it would also be considered a bedroom?

Is the house on a city sewer system or do you have a septic tank? If it is the latter, that might be an issue with permits. You need to do some local research.