Both sides keep TLS verify callbacks per context. Keep this side's
storage, which lets a handshake keep the callback it is running and
takes an exception from it as a rejection, and take the other side's
apply_verify_mode(), which works out the verify mode in one place on
every backend, with Mbed TLS and wolfSSL client contexts verifying by
default. Mbed TLS installs its verify callback on every session, and
each session runs its own copy of the user's callback. The redirect
client setup that both sides added is kept once.