My question is: How do I stabilize this crack?
Can I fill something into the hole so that the crack doesn't get any worse?
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Put glue-ca or wood glue in now, back out the screw and then predrill and lightly countersink so the screw will hold but not force wood apart.
The rule with splits or breaks like this is
Don't skip #2 or you'll have wasted the glue. Clamping forces the glue into the wood, and it will be a stronger bond when cured, than the wood alone would be.
I would remove the screw, glue, clamp, and then take a drill bit the size of your screw head and chamfer the hole (just rev the drill and press lightly to let the drill cut a bevel where the head will sit). The chamfer should ensure it doesn't crack when added again.