It depends. Sometimes the authors retain the rights either through a less restrictive publisher or through self-publishing and can set terms for their works, while other authors cannot.

In your example, Kodansha may own the right to publish the manga in their magazine but that doesn’t always mean they own the IP for that manga. So if Kodansha decides to publish an issue of their magazine that has that manga in another country, they can, but they may need permission from the mangaka depending on how the rights were sorted. However, Kodansha may not own the IP rights and could therefore not release the individual manga. This is generally all stuff stipulated through contracts, and a particularly influential mangaka may get more leeway with a less restrictive contract over someone new or without a track record.

This gets even messier when multiple people or companies own partial rights to an IP. In those cases, usually one company just stops caring but refuse to sell their share, and the IP effectively dies forever.