Upon looking further, I see two more things:
– the issue is only showing up when attempting to access /wp-admin/ or if one is logged in; anonymous sessions still work
– that 4.7.8 introduces the use of PHP namespaces, which were introduced in PHP 5.3.0; however, my webserver only as 5.2.17 installed at present.
Given how long in the tooth PHP 5.2.17 is, I see if I can get the host to upgrade.