I am also experiencing similar problem when using Cisco AnyConnect VPN client — some sites can be unresolvable, but after resetting mDNS (sudo killall -HUP mDNSResponder) they start to work again, for some time, or other "behind" VPN may become unresolvable.
The most irritating though is that during these problems, nslookup can always resolve the hostname while following ping will refuse to resolve.
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Have the similar problem with 14.0 (16610.1.23.1.3) on Big Sur build 20A5343j. Safari actually starts but within a second hand, does not crash though. So far I couldn't make it work by either preferences/caches/support folder deletion or even installation of Safari TP (the latter does exactly the same).