Put in a shelf at closet hanger height starting just past the door swing with baskets above and hooks below.

Is the porch heated if so adda closet there and make that the entry. A foyer is exactly what you have which is great for welcoming guests but sure can’t hang up coats or put shoes anywhere.

Is this your family's primary entrance, or mostly for guests? (Does your family tend to use the garage entrance instead?)

This is the primary entrance yes. Porch is a stretch for what it is- which is an issue in itself. But here are the photos

Ikea has several narrow shoe cabinet options on the market, and there are plenty of others out there. Maybe you can find a product with the right dimensions to give you some shoe storage and a drop zone on top, with hooks above if needed.

This one with feet would allow clearance over your floor vent. It's a little too deep to fit behind your door, but might work centered on the wall. https://www.ikea.com/us/en/p/hemnes-shoe-cabinet-with-4-compartments-white-60156121/

This one is skinny enough to fit behind the door, but a tad too long to put a pair in the space.

https://www.ikea.com/us/en/p/hemnes-shoe-cabinet-with-4-compartments-dark-gray-stained-30381753/

Neither will hold very many adult shoes, but could give you storage for a couple of adult pairs and several children's pairs.

Here's a picture of Idea products.

There are pros and cons for each of the racks. The one on the left hides the shoes but I find the one on the right easier to use and clean also. Looks like you could use a rack to hang hat/s coats on.

You also need a bigger rug. That one is way too small.

What size rug should we use for this foyer? Also- I have been considering these ikea shoe storage cabinets but then become confused with how It impacts the dining room flow

You could do so much with that entry! I would get a bigger rug and you could do a console table with baskets under for shoe storage and a tray on top to hold keys, with a lamp and mirror or art

you could do a bench so kids could sit and put hangers above to hold coats/ hats

Another option to consider would be an entry bench or a hall tree with shoe storage underneath - that gives you a place to sit (other than the stairs) and take off boots.

https://www.wayfair.com/furniture/pdp/gracie-oaks-verdi-hall-tree-with-bench-and-shoe-storage-grcs7389.html

https://www.wayfair.com/Greyleigh%E2%84%A2--Cainsville-Shoe-Storage-Bench-X114327387-L256-K~W003216276.html?refid=GX434287247006-W003216276_473363386&device=c&ptid=911017978782&network=g&targetid=aud-354999624671:pla-911017978782&channel=GooglePLA&ireid=94437635&fdid=1817&PiID%5B%5D=473363386&gclid=Cj0KCQiAoab_BRCxARIsANMx4S5P7yfLlM4zNr2XVNc5ZQ0u-iEZdhYSKWhLUu4JuQYE7k-sNbSMfQkaAuQNEALw_wcB

I would remove that piece of furniture on the right in the dining room so you can

walk a straight line into the kitchen. You now have to zig zag (I think).

Perhaps move it to the front door area and use it to hold shoes etc. Perhaps a mirror above and

basket for keys etc. Perhaps move that odd chair in the dining room to the front door, so one can

sit down and take off shoes.

At least twice the size of that mat, and big enough to put the shoe tray on.

Give it a try. Might work out.

Depending on what else you decide to use, this cute Ikea coat rack might add hanging storage at kid level behind your door.

https://www.ikea.com/us/en/p/tjusig-hanger-black-80291707/