Costs versed pratcality of adding half bath

Well you already have water available from the wash machine area so it would be a matter of adjusting the plumbing and I would assume there is a drain near the wash machine as well for a sink and/or shower. Where you would run into a greater expense is if you added a toilet--for the waste water--you would need separate plumbing for that. It would probably be a few thousand dollars once you add up a vanity/sink, a shower stall, plumbing, paying the contractor, plus any other things like new flooring, wall paint, bathroom fixtures, and new light fixtures.

How expensive is too expensive? Do you plan to do the work yourself and have it done? What (if any) plumbing will you need to run? Is the room you are considering doing this in just need a potty and place to wash your hands? Are you going to put new flooring in?

You can add some really nice outside showers inexpensively, YouTube has lots of designs and videos...... https://www.youtube.com/results?search_query=how+to+create+a+outside+shower+for+pool

Costs vary by region and even communities. First would the building codes allow it. Would be the first thing to check. They also can advise you where it can go. They can also refer contractors that have done work in the area. Plumbing would more likely be the biggest expense. Especially if there is no basement or crawlspace.

I think you could have a toilet installed there pretty inexpensively, since it looks like a lot of the plumbing is already nearby. It will depend on if there is a tie-in close by for toilet flushing. I would consider just a toilet added in the laundry room if you can have enough privacy, we have a pool and our outdoor bathroom is currently out of order - it was so much nice when we didn't have to go inside through the house to use it! I'm not sure what the last photo of the outside area is?

HomeAdvisor.com or Angieslist.com can provide a list of reference verified contractors... who can give you information and estimates on putting in a powder bath.... You might also consider putting in stackable front loading washer and dryer it may help with the floor plan and allow space for that new powder bath.

Cost to have a new toilet, vanity, shower $26000 if you can't do any work Have a local plumber come look at the drains. You can order a sink built into a vanity, small toilet and flooring by shopping hard for price and quality. Do you want a shower? Shower pan and install about $4200 but you also need doors, tile or built-in surround to be cheaper finding a small used claw foot tub which goes with your Cape Cod theme but men will frown on the resale value of this. Where are you moving washer dryer? Outside?

A floor plan would have been more helpful than the photos. It's not just a matter of enclosing a space; you have to consider how you would extend a roof over the space. The outdoor area you show would require major changes in roof pitch, or the use of a flat roof. You could gain space in your laundry by stacking a front loader washer and dryer. You would be spending a lot of money on new appliances, and you would lose the cabinet currently over the washer. It would, though, be simple for the plumber to extend hot and cold water lines from the washer hookup. You would get a small but usable half bath.

Caroline's numbers re: cost look right to me. Yes, the most expensive part will be the plumbing for a new toilet. William raised a good point about the expense being greater if the house is not on basement or crawl space. Mindshift has a good point about the roof pitch having to accomodate the new addition.

Consider a cassette or composting toilet. This eliminates the plumbing and they are excellent products.

I don't know anything about them but there are upflushing toilets, that cost more upfront, but apparently cost less to install where the current rough in doesn't exist. https://www.bobvila.com/articles/429-adding-a-basement-bathroom/

With a pool in the backyard, I would say that having a half bath (toilet, shower, and sink) accessible on the same level is high practicality. However, I understand your concern about the cost ratio. You have approached the project in a sensible and right way- start by asking lots of questions, reading, and continuing to learn. It is better to take a little more time on this stage, and be sure about your decisions rather that just 'jumping off the deep end' into the project and then half way through, find you are water above your head. (I couldn't resist that analogy.)