Bredts rule is only for carbocation or free radical ....why not for carbianion

Bredt's rule is an empirical observation in organic chemistry that states that a double bond cannot be placed at the bridgehead of a bridged ring system, unless the rings are large...

Bridgehead carbanions are not planar, but in fact, pyramidal. So, they are definitely not sp2 and hence, the Bredt rule isn't violated. Bredt's rule is for sp2 hybridisation.

Because Carbanion is SP3 hybridised so it can exist at bridge head position.. Bridts rule is applicable only for sp2 hybridised carbon i.e., carbocation or alkene which is planar ...