What mudroom features do you want to have? What's in the closet? How many people go through the door to the garage several times a day?

Id want to include a bench and some hooks. need closed storage where i would keep laundry baskets while not in use. 4 people live

Doesn't look like a lot of space to accomplish those goals, though not sure what's in that closet next to the dryer. If you would consider removing the laundry sink and buying new front load stackable washer & dryer, then that would open up space for you to add your wish list items. May require relocation of plumbing and electrical.

Lot's of ideas.

(i'll address the closet in another comment) Right now, the sink and the appliance wall and floors:

sink is always good to have. I wouldn't get rid of that. You can do something more vintage looking,

Paint your cabinets, do a wall of subway tile (or any tile) get a drop in farmhouse sink, cabinet base

Or how about this makeover for $100?

https://timelesscreationsmn.com/diy-utility-sink-makeover/

This one is cool too.

You could do a shelf over the back of your washer dryer.

see how they did this one? super easy w/a 1x8 piece of wood and pipe parts.

or just support it w/brackets into the studs.

other sink and wall ideas

Love these colors. find a sink like this, a sink base (get a used one, modify it and paint it)

add the shiplap surround (to do it on the cheap, buy the cheapest pine floors from Lumber Liquidators, (it's less than $3 a sq foot) and put it on the wall. prime and paint. I used it on the walls inside our trailer. looks great on the wall, the ceiling )

Do a cool shelf above the sink.

For your floors, Paint and stencil the tile.

Before and After. (go to Royal Design STudios, or CuttingEdgeStencils for tutorials)

Part II.

remove that closet.

don't know if you can take down that wall next to the dryer. if you can, great.

all sorts of ways to do a bench, wall hooks, cubbies, etc.

this is Ikea. Look up "ikea hack mudroom bench"

if you can DIY, you can easily build this w/plywood and MDF.

shiplap or beadboard, attach the hooks, paint above it. add shelves and or/cubbies

board and batten. wood bench. hooks. super simple. bring in some baskets for under the bench, maybe some vertical cubbies on the side for shoes

don't know if you want to retile the floor, but there are a ton of designs you can do.

I'd paint the door a dark color (depending on what design you go with.

Find remnant tile leftovers on craiglist or tile stores, or clearance sales.

if you like the shiplap, do the pine flooring like I mentioned.

look up DIY laundry room makeovers and see what you like.

if you want to keep your vintage cabinets, give them a sanding and stain, clear coat, new hardware. Try some larger pulls