mesh: switch the routes controller to use the controller cache instead of bimappers

[rboyer]

Description

This switches the routes controller from using the custom bimapper caching to using the common controller caching system.

Testing & Reproduction steps

• The existing tests were retained.

PR Checklist

• [x] updated test coverage
• [ ] ~external facing docs updated~
• [ ] appropriate backport labels added
• [ ] ~not a security concern~