Add documentation clarifying trailing slashes for basename (#37580)

Author: musm

base/path.jl

@@ -165,10 +165,17 @@ See also: [`basename`](@ref)
 
 Get the file name part of a path.
 
+!!! note
+    This function differs slightly from the Unix `basename` program, where trailing slashes are ignored,
+    i.e. `\$ basename /foo/bar/` returns `bar`, whereas `basename` in Julia returns an empty string `""`.
+
 # Examples
 ```jldoctest
 julia> basename("/home/myuser/example.jl")
 "example.jl"
+
+julia> basename("/home/myuser/")
+""
 ```
 
 See also: [`dirname`](@ref)