How do I make the front entry more functional?

Hi Lynn, great space! Is there room in the closet to hang everything inside? You could replace the doors with ones that are not slatted and put hooks on inside of the doors for easy hanging. If not, is there room to put a storage piece with a bench where the coats are hanging now? The coats would hang in/on it and shoes would go in cubbies below. I would also remove hooks by front door and hang artwork there. Everything would hang on the storage bench. https://www.hometalk.com/diy/build/furniture/diy-mudroom-bench-7243857

DIY Mudroom Bench

A hall tree might be just what you need. They have hooks for coats and such and storage under the seat for shoes. It also has the added advantage of a seat for putting on shoes.

I would clean out the closet and keep only what is needed for that season. Hang coats in there and get rid of all of the hooks. Replace the louvered doors and install solid doors. Put hooks on the inside for bags and other things you have hanging around. Put a bench with storage under it, where the chest is. Put the shoes in the baskets. Like this:

https://www.wayfair.com/furniture/pdp/beachcrest-home-mckinley-storage-bench-seho1471.html?piid=15049389

Hang a decorative shelf with a mirror, above it for keys, wallets, etc. Like this:

https://www.wayfair.com/decor-pillows/pdp/red-barrel-studio-hallas-wall-organizer-mirror-rdba3182.html

As for the second picture, it looks like you have a lot of things in the room. Maybe just declutter and rearrange the furniture (I really couldn't tell much as for the size of the room and how everything was arranged from that picture).

Take the closet doors off and leave closet open. Its creates an easier and more accessible place to put items. I would use hooks rather than hangers. Tall and low hooks if you have children. Use the space only for items being used. Floor of closet use for shoes, a shelf could be added to increase space. Out of season items store in a serapate location to reduce clutter. I know it sounds lazy but no one really wants to open a closet door. The hooks makes it easier to quickly hang items.

I agree with others, take off the slatted doors and replace with solid doors.

Or you could take the doors off altogether and build a shoe store bench below with decorative hooks around the inside of the alcove above.

If you have no option to keep the doors, I would paint them white to blend in with the wall.

I think a little differently. I'd clean out the closet - remove all hooks, etc. from the walls. What doesn't fit in the closet - current season hats, coats, shoes/boots only - goes into each person's bedroom. NO excuses. The only way to stop it from looking cluttered is to remove the clutter. Anything else is just rearranging it.

We added board and batten to our entryway wall (see it here) and you could also add hooks to it to make it super functional. And it would look cute, too!

Take the closet doors off and leave closet open. Its creates an easier and more accessible place to put items. I would use hooks rather than hangers. Tall and low hooks if you have children. Use the space only for items being used. Floor of closet use for shoes, a shelf could be added to increase space. Out of season items store in a serapate location to reduce clutter. I know it sounds lazy but no one really wants to open a closet door. The hooks makes it easier to quickly hang items.