SNAFU with indexed properties & type extensions: internal error & inconsistency over shadowing

The modality of calling indexed properties and shadowing are a bit mixed up:

let mutable i = 0
type T() =
  member x.indexed1
    with get (a1: obj) =
      i <- i + 1
      printfn $"T().indexed1 {a1} !\t%03i{i}" 
      1
    and set (a1: obj) (value: int) =
      i <- i + 1
      printfn $"T().indexed1 {a1} <- {value} !\t%03i{i}"

module Extensions =
  let mutable j = 0
  type T with
    member x.indexed1 
      with get (aa1: obj) =
        i <- i + 1
        j <- j + 1
        printfn $"type extensions aa1 {aa1} !\t%03i{i}\t%03i{j}"
        1
      and set (aa1: obj) (value: int) =
        i <- i + 1
        j <- j + 1
        printfn $"type extension aa1 {aa1} <- {value}!\t%03i{i}\t%03i{j}"
let t = T()
t.indexed1 ["ok"] <- 1           // calls the intrinsic property    
t.indexed1 ("ok") <- 2           // calls the intrinsic property    
t.indexed1 "ok" <- 3             // calls the intrinsic property    
t.indexed1 "ok"                  // calls the intrinsic property
t.get_indexed1 "ok"              // calls the intrinsic property
t.set_indexed1 (a1="ok",value=1) // calls the intrinsic property

open Extensions

t.indexed1 "nok"        // calls the intrinsic property?
t.indexed1 (a1="ok")    // calls the intrinsic property
t.indexed1 (aa1="ok")   // calls the type extension property
t.indexed1 ["nok"] <- 1 // calls the intrinsic property?
t.indexed1 ("nok") <- 2 // calls the intrinsic property?
t.indexed1 "nok" <- 3   // calls the intrinsic property?

t.get_indexed1 ("nok") // calls the intrinsic property?
t.get_indexed1 ["nok"] // calls the intrinsic property?
t.get_indexed1 "nok"   // calls the intrinsic property?

t.set_indexed1 ("nok_015",1)          // calls the intrinsic property?
t.set_indexed1 ("nok_016",value=2)    // calls the intrinsic property?
t.set_indexed1 (a1="ok_017",value=1)  // calls the intrinsic property
t.set_indexed1 (aa1="ok_018",value=1) // calls the type extension property

t.indexed1(aa1="nok") <- 1 // error FS0073: internal error: The input must be non-negative. (Parameter 'n') (ArgumentException)
t.indexed1(a1="nok") <- 1 // error FS0073: internal error: The input must be non-negative. (Parameter 'n') (ArgumentException)

also, there is an internal error when attempting to call indexed setter when specifying the argument name.

observations:

F# supports overload resolution of type extension based on the argument name (we can support smalltalk APIs!)
calling a setter with argument name is always causing an internal error
the shadowing rules are mixed up (all the "nok" that don't result in internal error)
it is not possible to call the type extension setter with argument name, resulting in asymmetry with getter syntax

dotnet / fsharp

SNAFU with indexed properties & type extensions: internal error & inconsistency over shadowing #16034