SearchForSingle versus SearchForMany leads to confusing results sometimes

As a user, I find the difference between SearchSourceForMany and SearchSourceForSingle quite confusing. Take a look at this for example -

PS C:\WINDOWS\system32> winget search resourcehacker
Name            Id                          Version
---------------------------------------------------
Resource Hacker AngusJohnson.ResourceHacker 5.1.8
PS C:\WINDOWS\system32> winget show resourcehacker
No package found matching input criteria.

Search clearly returned a single result, so why wouldn't show also find that single result? Is this actually a bug in SearchSourceForSingle?

_Originally posted by @Trenly in https://github.com/microsoft/winget-cli/pull/2847#discussion_r1068944891

SearchForMany searches more fields with substring search, SearchForSingle on the other hand, searches only PackageName, Id, Moniker, PackageFamilyName and ProductCode with CaseInsensitive search, which is more strict and less likely to return multiple results.

Originally posted by @yao-msft in https://github.com/microsoft/winget-cli/pull/2847#discussion_r1068954278

Feature Request

There are times when SearchForMany will return a single package. When it does, it can make moving from a command like winget search resourcehacker (which returns a single result and uses SearchForMany) to a command like winget install resourcehacker (which returns no results and uses SearchForSingle) very frustrating for users.

Implemetation

My first thought is to start with a search for many. If search for many returns only one result, use that result. If search for many returns multiple results, then fallback to search for single. One downside to this is that if there is only 1 package returned from search for many, it has a higher likelihood of not being the package the user intended due to the additional fields being considered in search.

Second thought is to add a setting for a default query. Neutral/Unset would be the current behavior - some commands use search for single, others use search for many; Strict could be always using search for single; Broad could be always using search for many

Third thought would be to instead have an argument that could be added to make the search for single a bit less restrictive, perhaps using a substring search instead of a case insensitive search while still ignoring the additional fields considered by a search for many

Start by reading the SearchSourceForMany and SearchSourceForSingle entry points and reproduce the winget search resourcehacker and winget show resourcehacker behavior. Compare their matching rules and review the three proposed approaches; the work is done when one behavior is selected, implemented, and covered by tests for single-result and multiple-result searches.