Is your feature request related to a problem? Please describe.

For secondary tenants, we use a rangefeed-backed mechanism to initialize and watch cluster settings. On the system tenant we use the older gossiped system config. This is unfortunate because we want to stop gossiping the system config (#70560).

Describe the solution you'd like
We should adopt the same code for the system tenant that we use for the secondary tenants.

Additional context

There's the beginnings of a WIP for this in #69269.

Epic CRDB-10489