Also note that "upgrading a dependency" is a relatively rare occurrence in the sense the I understand the question. Google definitely uses third party code but it is outstanding how much is proprietary Google owned and authored. For this code you don't release new versions and update, instead you evolve APIs gradually (as the other commenters have explained).

For third party dependencies there are two main options.

1. Do it all at once. This is good for relatively small numbers of users or small API changes.

2. Introduce the new version, migrate users, then delete the old version.

Note that for third party libraries Google does maintain a fairly strict one version policy so 2 is always a temporary measure.

https://opensource.google/docs/thirdparty/oneversion/