PHP Fatal error: Call to a member function get() on null in /wp-includes/cache.php on line 123

That line 123 references the WordPress object cache, see https://github.com/WordPress/wordpress-develop/blob/7c38750b162c784d92f54d9a36044c0f5318fe24/src/wp-includes/cache.php#L123

Sounds like you have an external object cache (Memcached, Redis, etc.) that isn’t set up properly or a plugin that wrongly modifies WordPress’ internal object cache (which is basically a no-op). This could be configured by your host too.

Try disabling all plugins to see if this still happens.

Your Woo Sync error sounds completely different though. You should ask about that in a separate thread if needed.