We have our own database of every version of every rubygems package alongside its runtime dependencies (like you see at https://rubygems.org/gems/pundit).
Then we parse your Gemfile and Gemfile.lock. We use the Gemfile to figure out gem group and pinned requirements (we run turn your Gemfile into a ruby AST since Gemfiles can be arbitrary ruby code; we use bundler's APIs to parse your Gemfile.lock). This gives us all of the dependencies your rely on.
Then we let you choose one or more package that you want to upgrade and the version you want to target (let's say Rails 7.0.4.3).
Now we have [your dependencies and their current versions], [target rails version], [all of the runtime dependency constraints of these gems]. We run this through a dependency resolution algorithm (pubgrub). If it resolves then you're good to upgrade to that version of Rails without changing anything.
If this fails to resolve, it's because one or more of your current dependencies has a runtime restriction on rails (or another indirect gem being pulled in by the new rails version). This is where the optimization part comes in. The problem becomes "what is the optimal set of versions of all your dependencies that would resolve with the next version of Rails". Currently we solve for this set trying to optimize for the fewest upgrades. As our dataset of breaking changes gets better we'll change that to optimizing for the "lowest effort".
Happy to elaborate.