[Non-Pro here] It looks like you'll be losing a window in a space that already appears very dark.

Also, the closet that you plan to add will eat up into the (already fairly narrow?) sunroom, so that may limit the option to e.g. set up a nice sitting area there, etc., and you'll lose the window's symmetry within that wall which may look weird.

I'm wondering if that would be a turn off for future buyers in a way that will not increase the property value despite the extra bedroom.

There's a chance that the community may have additional ideas for you if you can post a 2D to-scale layout of your house (or at least the space in question).

To give good advice, you need to post a diagram with dimensions of the rooms, windows, and wall openings (give us the full living room and sun room, as well as proposed remodeled sizes), A proposed budget and info on whether the sunroom/living room wall is load bearing would be helpful too.

Have you thought about taking half of the sunroom (where you might have the closet), putting the bedroom towards the front of the house, and then having the closet on the back/solid wall of the living room? It doesn't appear that you have allowed enought space in the sunroom for a closet. That means, by the time you build a useable one, you will have eaten up much of that side of the sunroom anyway. Might as well make it a useful space.

That would be a lot of bedrooms sharing 1 bath.....hmmmmm....

Floor plan needed.

Looks like the living room is very narrow, and not all that large to begin with. Creating another bedroom, and taking away a portion of the sun room, would be a turn off, and in mind, would devalue the house. I would leave it alone, and paint up the rooms you have, and make them look as nice as you can, is what will bring value to your home.

IMO a bedroom needs a bathroom close by not a trip through the LR to get there . I agree you have a small house and the need for this bedroom needs to be explained . IMO this is nice little house fix it up to be exactly what it is . Bumping into the sun room would not be a good idea either .

Post a 2D floor plan of the whole house with all doors, windows, etc noted. We can't determine from dark photos whether it could work or not, although I'm inclined to agree it's a bad idea.

I greatly appreciate it everyone comments on this topic. I will not be adding a third bedroom and will look to improve the existing area and what work with what we got ! P

Paint and remove the carpet and the space will look a lot better. The brown is bringing the place down. Maybe there are hardwood floors under the carpet? The one end of the living room might make for a good home office, which wouldn't require a closet - if you need one. No need to make changes for a mythical future buyer.