Reddit mentions of Hudson Exchange 4010 Classic Boot Tray Mat, 34" L x 15" W, 3/8" Thick, Medium Brown

I would put a freestanding hall tree against the wall beside the door or floating along the carpet line. Coat racks are fussy and I think you'll need something substantial as the kids grow up. Plus, you can usually add a lower second row of hooks (that kids can easily reach) on anything with a reinforced backboard.

Don't set the hall tree on the tile because your walkway is very narrow. Get one with built in storage so there is a place for the bags to sit on top and baskets underneath for accessories. This won't be used as seating, just bag and accessory storage. Open baskets on a shelf work best, no more than 2/3 of the shelf height so a hand can grab something inside without too much hassle.

Here's an open style with plenty of shelves for storing accessories:
HOMYSHOPY Entryway Hall Tree with Removable Hooks, Storage Shelves and Bench, Multipurpose Coat Rack for Hallway, Vintage Brown https://www.amazon.com/dp/B07PR8LHVK/ref=cm_sw_r_cp_apa_i_artQDbX5XJG9W


Here are two more traditional ones that might work:
Crosley Furniture Seaside Hall Tree - Distressed White https://www.amazon.com/dp/B01MG6URP0/ref=cm_sw_r_cp_apa_i_FstQDbTC40RPM


Linon 76063ANT01U Santa Fe Hall Tree, 40" W x 17.99" D X 64.02" H, Natural https://www.amazon.com/dp/B010PBECF2/ref=cm_sw_r_cp_apa_i_yttQDbMR8HG1X


Remove the coat hooks from the wall and line stacked shoe storage along the short wall, maybe a tray next to them since men's shoes and winter boots don't always fit the dimensions anyhow. Plus, it just looks tidy and is a good reminder for where shoes are allowed to go. I recommend keeping all shoe storage open because you want to keep your system painless for children or newcomers to use.

Personally, I like shoe shelves that aren't just the skinny bars because small shoes and heels don't stay on easily.

To match the first hall tree, 1 or two of these depending on space:
VASAGLE Shoe Rack, 5-Tier Shoe Storage Organizer with 4 Metal Mesh Shelves for 16-20 Pairs and Large Surface for Bags, for Entryway, Hallway, Closet, Industrial, Rustic Brown ULBS15BX https://www.amazon.com/dp/B07SJZJ7YK/ref=cm_sw_r_cp_apa_i_4vtQDb470GXYV

Different styles:

MyGift Rustic 4-Tier Vintage White Wood Entryway Shoe Rack Storage Shelves with Handles https://www.amazon.com/dp/B07JYM9M5R/ref=cm_sw_r_cp_apa_i_zBtQDb3JCZX2T


LANGRIA 4-Tier Metal Shoe Rack Utility Shoe Tower Shoe Organizer Shelf for Closet Bedroom & Entryway Bronze https://www.amazon.com/dp/B01EJO9UP8/ref=cm_sw_r_cp_apa_i_qztQDbN43B2HT

Boot tray options, but take measurements first:

Hudson Exchange 4010 Waterhog Classic Boot Tray, 34" L x 15" W, 3/8" Thick, Medium Brown https://www.amazon.com/dp/B00TT8ESRK/ref=cm_sw_r_cp_apa_i_mDtQDbHGWT34G


Ottomanson TRY400-30X15 Multi-Purpose Indoor & Outdoor Waterproof Tray, 15" x 30", Black https://www.amazon.com/dp/B01LBL9XKE/ref=cm_sw_r_cp_apa_i_sEtQDb184SCKD


I would move the wood bench either behind the floating hall tree, floating in front of the hall tree against the wall, or along the wall by the other doorway if it stays in this area at all. You might need to play around with a few layouts and see what works, and if course measure and verify that everything works for you. The examples I linked are not vetted, only style suggestions and they might come in different sizes and quality ratings from other sellers.