The bedding looks good, usual factory job,
assuming the tang is relieved, and the Mauser spacer is around the rear action screw.
That acts like a pseudo pillar to prevent wood compression at the rear of the action.
Putting a real, fixed pillar at rear never hurts.
The Mauser bolster around the front action screw can also be made to fit inside a larger pillar
if you really want to gild the lilly.
But you need a cross bolt through your cracked web.
A tiny brass pin like Remington uses is not as strong as a hidden piece of steel allthread.
"Dressing down" the brass pin's exposed ends might end up with needing to refinish entire stock.
The steel threads on bolt shown here is 0.234" OD (15/64").
Cut off the head of bolt and you have over 2" of allthread to work with:
The 1/2" allthread shown above, can be used as a long axis rod in grip.
Whatever wood is removed in the cracked web area will be filled in with epoxy and steel.
Stronger than when new.
Get a Dremel Tool with a wood-cutting spud and start undermining into the sides of the web on either side of the crack,
then make the holes meet in the middle and keep hogging until the allthread will lie in the trough,
below flush. Then fill and cover all with a good epoxy.
Release agent on floor plate to flatten the epoxy to flush.
Or press any flat surface with vinyl tape wrap and release agent over the epoxy to flatten flush as it hardens.
This is not a critical bedding surface.
JB-Weld Original Formula is excellent for this.
I have done entire barrel channels and actions with it on synthetic and walnut stocks.
The hidden allthread also works well behind barrel recoil lug to further gild the recoil lilly,
use 3/8" or 1/2" diameter there: