I would go with a 24" sink as deep as I could get it or not bother with one. A standard oval bathroom sink is 16" wide. A size 10 shoe is almost 11" long. Not much room to maneuver in 15" and actual bowl size can be smaller than sink size depending on the style. If it's placed in a cabinet not that much space is lost. Smallest sink cabs are 18" when you can find them so it's only a 6" difference.

Utility sinks are deep because they would be perfect for cleaning up all the messes you mentioned plus! I would not be w/o one. I've never seen a washer that dumps into one.

"I've never seen a washer that dumps into one."

My mom had that set-up when I was growing up, as did I in my previous two houses.

I could get a 24" sink in the space no problem, but I would have to forgo my wish for a broom/coat closet cabinet bank.

My other option is to stack the machines, but I really don't want to do that, mainly because of the machines I want (compact Miele on pedestals, this set up is perfect height for me -- tall enough so no stooping/bending but not so tall that I can't make use of counterspace on the top), plus if I stack the machines I lose counter space.

I guess it's all a compromise. There's nothing wrong with coats on pegs like they are now, but I do want it all behind closed doors.

It could be just me but I like having hooks to hang coats and jackets that are in use. We have a coat closet but I only store clean out of season outerwear in it. My jackets get damp and dirty and I like to hang them on hooks to dry or air out. To my way of thinking, behind closed doors invites a musty closet at best.

It's always a compromise. I actually decided to leave the washer and dryer in the garage for now to use the 5 foot space I'd designated for them for my saddle and tack and additional floor space.

Try and fit in a utility/laundry sink that comes in a cabinet/vanity. Most cabinets are 24" wide. You can get it in stainless and it is a deep sink. This one is at Home Depot. I like the stainless edge for messy items. Makes it easy to clean.

We have a stainless steel 15" laundry room sink that is 6 or 7 inches deep. It sits in a vanity type cabinet and that is all the space our laundry room affords us. I never had one before this house and it has functioned well enough for my needs. I'll take it over nothing and am very grateful to have it. Better a small one than nothing at all.

Measure the various things that you might want to wash in said sink and go from there. I have a 28" shop sink in my basement that I use to wash big stuff like grill grates and the water pan for my smoker so we don't need a big laundry sink.

Yes, 15" is too small for a laundry sink.

Think of all the things you can't put in your kitchen sink, but need to wash occasionally.

It would be nice to have a sink you could.

I think a 15” sink would be better than none at all. Ours is 17” and 12” deep.

I guess I should have mentioned in the original post that I have a very large utility sink in the basement, it's one of those 40" jobbies. But yea, getting out the measuring tape and measuring cleaning buckets and misc smaller items we wash in the sink is a good idea.