`Base.Broadcast.promote_containertype` improvements

[TotalVerb]

As has been noted in the past, and again here, adding new containertypes to broadcast tends to involve adding many new methods. For example, in practice methods seem to come in pairs, one for each argument order. (see e.g. https://github.com/davidanthoff/DataValues.jl/pull/9/files#r113047389)

Perhaps we can borrow some techniques from number type promotion (e.g. the relationship between promote_type and promote_rule) to cut down on the number of methods needed.

cc @Sacha0, @pabloferz

[Sacha0]

Ref. #20007 (comment). Best!