Yes, the URL is on the public net, but unknown for everyone aside from you.
> Can it really be considered safe, a public URL; just because it's long
Yes: https://www.w3.org/TR/capability-urls/
Depends on the implementation of course. Many use the format of a UUID like this: 07463cd8-3f1f-11ed-b878-0242ac120002, although you should NOT! use a UUID, only the format or better something else.
But it is considered safe provided the link is only valid for a limited time (3 months should still be ok).
This mechanism should regularly be reevaluated though. It is especially security mechanisms that can compromise it. Corporate mail & firewall security will see the link, might log it somewhere where it can be exposed, etc.
But the fundamental mechanism is considered to be secure.
edit: The requirements for it to be secure are that mail and http access is secured by TLS of course.