Without serious dis-assembly you may never get it out.
It has soaked deep into the foam within the upholstery.
Cleaning solutions wetting from the surface will never soak deep in AND be able to be sucked out good enough.
The upholstery will need to come off the seat, turned inside out and cleaned from within.
If you're a good DIY it can be done with simple tools and a carpet ar shop vacuum. AND lots of time, like all day Sunday to do it.
If you 're paying someone to do it, realize it's a time intensive job and will cost accordingly ( ask for estimates )
-- how time consuming ?
- The seat base gets removed from the car.
- The seat backs too if the milk splashed there.
- Upside down on a work table, the hog rings and other retainers are removed to be able to "un-dress" the seat frame. The upholstery comes off, much like a tight fitting sweater, and is flipped inside out to expose the foam.
- Now hot cleaning solution is soaked in and vacuumed out. Possibly many, MANY different times. Use HOT water for better disolving of the dried milk.
- The 'good' side is cleaned again too and air dried.
- The seat springs/frame get cleaned.
- The floor and carpet previously hidden under the seat gets cleaned too.
- When dry the upholstery is re-fitted over the frame and hog ringed back in place.
- the seat base is re-installed in the car.
It's a lot of work.
The achilles heel here ? Yours exploded. You may be cleaning headliner, front seat backs, door panels etc.
I did mine ( just a spill ) myself with a shop vac that'll "suck a golf ball through a garden hose". This being an advantage over a carpet cleaner to really get the deep down sucked back out.