Cannot build project with z3-haskell on windows 10 - haskell

Question

I want to build the haskell bindings for z3 in a Cabal project, the following is the minimum (faulty) example:
Using a project initialized by cabal init:
test/
- Main.hs
- Setup.hs
- CHANGELOG.md
- test.cabal
With modified test.cabal:
cabal-version: 3.0
name: z3-test
version: 0.1.0.0
extra-source-files: CHANGELOG.md
executable test
main-is: Main.hs
build-depends: base >=4.14 && <4.15
, z3 ^>=408.2
default-language: Haskell2010
Z3 binaries are located at C:\z3-4.8.5-x86-win.
Z3-bindings are installed:
cabal v1-install z3 --extra-lib-dirs=C:/z3-4.8.5-x64-win/bin --extra-include-dirs=C:/z3-4.8.5-x64-win/include -v3
All the requested packages are already installed:
z3-408.2
Use --reinstall if you want to reinstall anyway.
Now building the project using:
cabal v2-build --extra-lib-dirs=C:/z3-4.8.5-x64-win/bin --extra-include-dirs=C:/z3-4.8.5-x64-win/include -v3
Results in the error:
Build profile: -w ghc-8.10.2 -O1
In order, the following will be built (use -v for more details):
- z3-408.2 (lib) (requires build)
- z3-test-0.1.0.0 (exe:test) (first run)
Starting z3-408.2 (lib)
Failed to build z3-408.2. The failure occurred during the configure step.
Build log (
C:\cabal\logs\ghc-8.10.2\z3-408.2-1722a25655334afbca91ac935f14ff0d20ccf8c4.log
):
Configuring library for z3-408.2..
cabal.exe: Missing dependency on a foreign library:
* Missing (or bad) header file: z3.h
* Missing (or bad) C library: z3
This problem can usually be solved by installing the system package that
provides this library (you may need the "-dev" version). If the library is
already installed but in a non-standard location then you can use the flags
--extra-include-dirs= and --extra-lib-dirs= to specify where it is.If the
library file does exist, it may contain errors that are caught by the C
compiler at the preprocessing stage. In this case you can re-run configure
with the verbosity flag -v3 to see the error messages.
If the header file does exist, it may contain errors that are caught by the C
compiler at the preprocessing stage. In this case you can re-run configure
with the verbosity flag -v3 to see the error messages.
cabal.exe: Failed to build z3-408.2 (which is required by exe:test from
z3-test-0.1.0.0). See the build log above for details.
How can I build a project with the z3 bindings?
Note that:
GHC version = 8.10.2
Cabal version = 3.2.0.0
I can only use cabal
Using cabal install ... or cabal v2-install ... results in Cannot build .. z3 because none of the components are available to build: