Cabal v2 Build inside Nix Shell does not see executables such as Alex, Happy (BNFC?)

Cabal issue. Discussion of how to fix! haskell/cabal#8434
Mine, already contains a fairly minimal example: NixOS/nixpkgs#176887
Same issue, some discussion of package-db: NixOS/nixpkgs#130556
Not the best but it has at least several comments reporting the error (and the title sums it up well): input-output-hk/haskell.nix#798
Same error but it isn't made clear in this one that the situation would happen even if Nix provides the tools, they seem to think it's a non-issue where Cabal is complaining because the tools were not provided: haskell/cabal#7197
Might be the same issue? input-output-hk/haskell.nix#839 Note in particular input-output-hk/haskell.nix#839 (comment) claims to be an explanation for this issue in general.
Simple duplicate. input-output-hk/haskell.nix#760
Simple duplicate, but also links an interesting question in the Cabal repo. input-output-hk/haskell.nix#1770

Only Tangential

Looks like a different issue, about "multi-libs" or something. input-output-hk/haskell.nix#1662 BUT! This comment by @andreabedini has insights into how Cabal is finding things: input-output-hk/haskell.nix#1662 (comment)
May or may not be distantly related: issues with haskell.nix running Setup.hs input-output-hk/haskell.nix#778
This may be affected by the same underlying cause, so notify them if and when it gets fixed: haskell/haskell-language-server#3128
Adds a disabled test that this issue is fixed. Notify them if and when it does. input-output-hk/haskell.nix#181
This is closed as a duplicate of the main Cabal issue. It does demonstrate that it affects testing tools too. haskell/cabal#8492
Closed as duplicate, but, affects testing tools and not just code generation or preprocessing tools: input-output-hk/haskell.nix#231
This looks like it's an unrelated issue about source-package-repositories, which merely happens to also occur in nix shells. (A user was linking to it as "the latest/current state of the issue" but it presumably isn't since it's not even the same one.) input-output-hk/haskell.nix#1367
NOT this issue; advice to use build-tool-depends rather than build-depends and whatever stopped even that from working was already fixed. input-output-hk/haskell.nix#398
Same error message but looks like an unrelated issue (Gentoo not Nix, and may be caused by mixing v1 and v2 commands). gentoo-haskell/gentoo-haskell#1074