None of the above will work.

You need to see if you can find another spot for either the washer/dryer and/or the hot water heater. We had an electric hot water heater in our condo and the difference in price was negligible.

Thank you for your response. Can you expand on why neither of them will work? We laid it out on the floor and all the clearances seem to be fine, at least theoretically. The price is not an issue, the average electric tankless water heater needs at least 120 amps to operate and the average household's total capacity is 200 amps.

1. Instead of putting the water heater in the bathroom, how about constructing a WH closet where the WH is shown in drawing #3. The door to the WH closet would be on the hallway, adjacent to the bathroom door. So-called "tall" WH have small diameters (e.g., a tall 40-gallon WH is only 21" in diameter). WHs are ugly and this would banish it from the bathroom.
2. With the WH in a closet, the bathroom door would be as shown in drawing #2 and one would walk down a short hallway to reach the bathroom.
3. One might position the toilet as the first component on the right-hand wall and (as shown in drawing #2), hidden from hallway view by the WH wall.
4. A neo-angle shower (example, example) might fit in the location shown in drawings #2 and #3.
5. A stacked washer/dryer might fit where it is shown in in drawing #2 but those are about 25" deep, a few inches deeper than side of the example neo-angle shower. Of course, you'd have to allow space for the doors to swing open.
6. You could position the sink as shown in diagram #1 but minimize its size by using a wall-mounted sink (example) instead of a vanity.

Would it all fit? Dunno. Tight!

ALTERNATIVE:

1. Put the washer/dryer in a closet instead of the WH. It's doors would swing into the hall.
2. Put this weird table top water heater in the bathroom where the washer/dryer would have been.
3. Erect shelves or cabinets over the WH.

ALTERNATIVE 2:

1. Put the washer/dryer in a closet instead of the WH. It's doors would swing into the hall.
2. Replace the neo-angle shower with a rectangular shower containing a sliding glass door whose operable side faces the bathroom's entry door.
3. Put a "short" water heater in a cabinet or closet where it is shown in drawing #1.
4. Erect shelves or cabinets over the WH cabinet/closet.

-- amateur

We need more info. Like what is on the other side of all these walls. Why a water heater closet cann be created outside the bathroom entirely. Or a washer/dryer closet created outside the bathroom.

If this is a cabin, why do you need 50gl of hot water?

"why do you need 50gl of hot water?"

It's Paul Bunyan's cabin. Babe lives there too.

Thanks for the comments. The bathroom has a bedroom to each side and the door side is next to the living room with a future staircase to the attic preventing any openings other than the bathroom door from that side. The only other option is to put it in the kitchen, which is already small, some don't really like that option. The whole place is only 700sf, so squeezing it all into the bathroom still seems like the best option even if it's tight. As stated above, the water heater will be 50 gallons MAX, but se also don't want to run out of water mid shower, so 40-50 was a recommended size.
I'll have to check out that table top water heater, that's a new one in my research.

I lived in an apartment where the water heater was under the sink in the kitchen.

Thank you for your response. Can you expand on why neither of them will work? We laid it out on the floor and all the clearances seem to be fine, at least theoretically.

1. How do you get into the shower? You have 9' in length. A shower should be a minimum of 3' wide. The toilet is in the way.

Plus you have 6' wide for the width of the room. That's 72". The vanity takes up 21" and the toilet takes up 30". That only leaves you 21" between the vanity and the edge of the toilet.

2. Again you have 9'. The shower takes up 3' and the toilet absolute minimum space side to side is 30". 36" is better. Add in the sink and you once again only have 21" in front of the sink to stand. Not enough room even for a child.

#3. The door won't even open all the way. Plus you have to dodge around the sink just to use the toilet. Not fun especially in the middle of the night.

The price is not an issue, the average electric tankless water heater needs at least 120 amps to operate and the average household's total capacity is200 amps.

So if price isn't an issue, you add enough amperage to cover the additional needs. That's what we did in our condo. Not a big deal.

You could invest in a tankless water heater to save space?

I don't understand why you can't use a tankless heater. What size electrical service panel do you have? Do you have room for two (50 amp) breakers, or three (40 amp) breakers? It might be possible to make room by putting in tandem breakers, or you could put in a larger service panel if needed.

"Cabin"? If it's located in a rural area it might be possible to construct a small lean-to type addition to contain the HW heater. What about the space under the planned-for attic stairs?

Thanks again for all the good feedback. Moving the water heater out of the bathroom will be a last resort if we just can't figure out a solution to keep it all in there, but I'm determined to try my best first.
The paper cutouts help with trying out different arrangements. My preferred option would be New #1, even if it makes the plumbing more complex. The water heater could be enclosed and have some towel storage above it, too. Using an 18" deep vanity should leave plenty of space to walk through (maybe I wasn't very clear in my original post, the width is 6' to 6'6"( that wall isn't in right now), so it is flexible where exactly it will land. I tried to use some actual product dimensions. Let me know if I am missing anything.
New Option 3 is just a more elaborate version of the previous idea. This is really the only one I can see that could have a plumbing wall and still keep everything in the bathroom. A sliding door in the shower should work better than a hinged one, it will be a tight squeeze, but should work, at least on paper.....
Option 3 is the one mentioned by wdccruise, where the water heater gets ejected.
Critique away if you have anything I should know :)