Is the door opening 65" or the closet interior, wall to wall 65"? If you can scootch one appliance over enough to then get the other one out, then It would probably work. You have to have enough depth. My closets aren't deep enough for a washer dryer set. take some graph paper and draw out a plan to scale and include the w/d set specs in the drawing, then you will know. If you have the depth, but not the width, you could always stack them. I have mine stacked in my bathroom and love it. I have another set in the basement side by side in the open, that works well too. If you stacked you could avoid the bifold doors, and have shelving on either side of the stack, along with a folding space, and possible hanging space.

I have laundry in the basement-- have a laundry chute direct to the laundry. I have never wanted a laundry on the second floor but have wished that I had it on the main floor sometimes. Advantage to basement--usually have a lot of room (I don't). We can get really dirty sometimes, with gardening and landscaping projects. Can shuck the dirties in the garage or back entryway and drop down the laundry chute there (or in a bucket in the garage)...vs having to deal with them upstairs (where we have carpet). I wash clothes once a week. Smelly dirty laundry is in the basement; not stinking up the bedrooms. I have a clothesline strung in the unfinished part of the basement for drying rugs, mattress pads, sheets, jeans, etc. during the winter/ rainy days. As well as drip dry items that don't go in the dryer. The clothes line is also handy for hanging wet or damp dirty items to dry (like bath towels & kitchen towels) before they go into the dirty clothes hamper. I fold & sort items as I unload the dryer. Towel stack to the linen closet, DS's clothes in one stack, etc. Usually cart the basket to the main floor and someone else will haul it on upstairs. Have had three laundries that were in enclosed back porches and one just adjacent to the garage when I lived in the south. That arrangement worked really good and would be my preferred location for a laundry. Would not want W/D in a closet if it can be avoided. I use my laundry sink a lot as well as having the washer drain hose empty into the sink. (With a lint sock to keep lint and dog hair out of the sewer line--septic leach field if that's your situation.) You adapt to wherever the laundry is. Pros & cons to wherever it is. Main thing is that a home laundry beats the heck out of having to go to the laundromat! We've probably all had to do that at some time in our lives.

@Jack D - Yes, like that, but can you move the W/D to the opposite wall that it is currently on and reframe the doorway closer to the "new bedroom" (might need a pocket door to laundry) perhaps shrink the laundry room a foot or whatever you can get making a bit more room for the closet system? I don't like the open closet system as I prefer the ones with doors. As a designer and a realtor, even though the room is small, you still have the extra room. I've got 5 bedrooms in my home and one of them is only 10 x 10. I've got a twin bed in there as well as a dresser. It's my sister's favorite room to stay in when she visits. https://www.ikea.com/us/en/p/pax-wardrobe-white-bergsbo-white-s19127297/?gclid=Cj0KCQiAkePyBRCEARIsAMy5ScuNAD-dsyPBUR5RMtwyJY550Nz6nsSDgCNi8biKdAOBwSi8dWbarqoaAr-8EALw_wcB

Hmm. the first thing I notice is two doors opening into each other at the garage entrance. Frankly Im a bit confused on the whole layout 1. do you really need two dining room areas? 2. do you really need two bathrooms on the main floor? 3. is the entrance to the mudroom only through the garage? 4. you have teenage boys but a playroom? why is that not the workout/office? I would be using that dining space as the office workout room having the workout room where everybody has to passthrough to the to the house is going to be annoying. and also doesn't give you any privacy.