From the release notes, there are no intentionally breaking
language changes between 1.12 and 1.13; however, 1.13
changes the behavior of tools for go modules that are
provided with the default language installation that may
break workflows that rely on the previous behavior.
The time required to migrate really depends on the project.
go projects that depend on private modules will require a
reworking of their bitbake recipe to indicate to the tools that
they should not attempt to use the default module mirrors to
download and authenticate the private modules.
For projects that do not use private go modules, it looks like
the changes to the tooling should be largely transparent,
although the release notes don't 100% guarantee that.