Consolidate and simplify usage of get_available_packages (#35556)

With recent changes where we largely switched to use primarily short
version of packages rather than `apache-airflow-providers-*` and
filters, there were several places where get_available_packages
family of method have been used inconsistently in various breeze
commands.

This change consolidates it all to commong way, it also replaces
the inconsistent `providers-index` with regular
"apache-airlfow-providers" - which is now not-ambiguous since the
package filters usage is not that much used any more.