Use a consistent version solve across devtools_server, devtools_shared, and devtools_app

Investigate doing something like what flutter/flutter does - solve for related packages at once, and them move those versions into the related pubspec / lock files.
This is probably not very high priority as we lock the versions of devtools_shared, devtools_common, and devtools_server to exactly match but this could help for some confusing edge cases where we might have a slightly different vm_service version on the server and app depending on how version solving went.

Related PR: https://github.com/flutter/devtools/pull/2229

Start by reviewing how flutter/flutter solves related packages together, then inspect the version-solving flow for devtools_server, devtools_shared, and devtools_app along with their related pubspec and lock files. Done means the packages are solved together and the resulting versions are moved consistently into those files, avoiding mismatched vm_service versions.

Written by the indexing model from the issue text.