Use a global `BaseClientBuilder` (#15548)
Alternative to #15105
Instead of building a `BaseClientBuilder` from `NetworkSettings` each
time we need a client, we instead build a single `BaseClientBuilder` and
pass it around. The `RegistryClientBuilder` then uses
`BaseClientBuilder` exclusively for configuration. This removes a chunk
of copy-and-paste code, and also moves the fallible `retries_from_env`
into a single place
Borrow vs. clone is mostly ad-hoc, we can change it in either direction
if it matters.
Closes #15105
