Waterproof Palladium Boots Frustrations

Howdy - so a few years ago, I purchased a clearance pair of PAMPA LITE+ RECYCLE WP+ Palladium boots in white. Foolishly, I thought they'd hold up in the rain but after a single outing, they ended up with mud stains seemingly underneath the pseudo-waterproof cover. I tried my best to clean them, gave up, and threw them in the back of my closet until today, when I decided I wasn't going to let them continue to taunt me.

Here's a link to the same model in yellow (white isn't on the site anymore, and were possibly clearanced for this very issue.)

Fabric details as supplied by manufacturer:

100% Vegan with no animal product in the upper including the glue

UPPER: waterproof shoe made in 100% recycled polyester

LINING: recycled polyester

SOCKLINER: 85% recycled foam + 15% PU / cover in 80% recycled polyester + 20% polyester

BOTTOM + TOE CAP: rubber with 15% recycled rubber / EVA / Rubber pads under the bottom to avoid slippery

I've wiped them down as best I can, given them a good scrub with dishsoap, and left them with a baking soda + water paste on (though I'm uncertain if that's even effective, given the waterproof poly shell.) I've been advised by Google Gemini to not put them in the washing machine or use Oxiclean but at this point, but i'll try anything that isn't certain to ruin them, as they're essentially unusable in their current dingy state.

Help!