Help users determine the origin of their ResolutionImpossible error

[nlhkabu]

I am currently putting together documentation for the new resolver (see #8459).

As part of this process, I've been trying to work out how a user would work out where in their dependency tree a conflict has occurred - because in projects where a conflict has occurred deep in the dependency tree, it might not be obvious what package(s) a user needs to look at to solve their problem.

#8380 went a long way to improving the default error message, however (as discussed with @pfmoore and @ei8fdb) it would be useful to expose more information in the error message itself.

Side note: suggestions in #8346 related to improving the output pip provides while resolving a dependency conflict could also help the user find the source of the conflict. I think we should do both.

Recommended message format to follow.

[brainwane]

Per discussion in our meeting last week, this is something we'd like to do in Phase III.

[nlhkabu]

Per discussion in our team meeting this week, I'd like this to be done before the new resolver becomes the default.

[nlhkabu]

Imagine that we have a situation where package_coffee and package_tea create a conflict, but both are being pulled in by other packages (e.g. they are not directly specified by the user).

Maybe we could illustrate the root of the conflict with something like this:

Due to conflicting dependencies pip cannot install package_coffee and package_tea:
- package_coffee requires package_water<3.0.0,>=2.4.2
- package_tea requires package_water==2.3.1

Conflict origin:
- package_cafe==2.1 requires package_iced_coffee==2.3.4
  - package_iced_coffee==2.3.4 requires package_coffee
    - package_coffee requires package_water<3.0.0,>=2.4.2
- package_iced_tea==3.4.5 requires package_tea
  - package_tea requires package_water==2.3.1

to discuss @pradyunsg @ei8fdb

[nlhkabu]

please see #8495 for most up to date error message suggestions.

[nlhkabu]

Closing in favour of #9036