Remove the old navigation code

Proposal

Once we've removed the toggle in #426893 (closed), the old header will be a dead code branch. We need to go through and remove it all. This is not only the header templates themselves but any left over switching logic, newly unused helpers, unused dependencies, old specs, and anything else that becomes unreachable as a result of replacing the navigation.

This task can be done slowly over time, but I'd recommend getting it done in one fell swoop. Probably across several MRs, but all in one effort. This should reduce the chance of us getting so far through and leaving stragglers.