Does anyone firing a rocket into space need to inform all world governments of it (i.e. not a nuke)?

Title kinda says it all.

When SpaceX or Blue Origin or Soyuz to the ISS or a whole bunch of others plan for a launch…

Do they need to phone every government on the planet (or at least the nuclear powers) to let them know that this is a scheduled launch, not a nuke, ignore your early warning systems for that spot at that time?

There are no nuclear missiles at Cape Kennedy as far as anyone knows, so why would a launch from there into space be considered hostile?

There is an international agreement called the Hague Code of Conduct against Ballistic Missile Proliferation of 2002 which requires pre-launch notification (unfortunately, the link provided in the Wiki article goes to a website in Japanese; a better online version of the text can be found here):

This obligation is on the state, not the company - as in most of international space law, launches are, even when they are done by private companies, deemed to be actions by a government (which authorised the private launch and which assumes strict liability for damages caused by the space vehicle).

To complement my previous post: Even prior to that multilateral Hague Code of Conduct, there was bilateral U.S.-Russian cooperation providing for pre-launch notifications; here is a 2000 memorandum of understanding between the two countries requiring such notifications - and providing some informatio on how, in practice, they would be made: They established a joint data exchange centre which would serve as the central hub for receiving and forwarding notifications based on “an agreed Internet-based technology incorporating, to the maximum extent feasible, commercially available equipment and software”.

Mobile launchers are a thing.

They can be launched from anywhere they can drive to (and sail to if you include subs).

And even before 2000, the spacefaring nations still preferred to notify each other, just with a less-formalized framework. This is not the sort of thing anyone wants misunderstandings about.

In the US at least, the FAA also publishes a NOTAM (notice to airmen) before scheduled launches.

ISS is a product of collaboration between countries so when they launch spacecraft to ISS I guess it is necessary to inform the collaborators about the launch. But if they decide on other space missions (which do not influence the Earth of course) there is a need to announce about it.

At the moment I think they’re only a Russian thing:
American Mobile Nuclear Missile Launchers Is a Really Bad Idea
Air Force Seeks Mobile ICBM Option