tkinter looks installed, but fails when imported

I really want to use matplotlib > 3.8.4, but it requires this solution which is not working.

My configuration:

PyCharm 2024.3 (Community Edition)
Build #PC-243.21565.199, built on November 12, 2024
Runtime version: 21.0.5+8-b631.16 aarch64 (JCEF 122.1.9)
VM: OpenJDK 64-Bit Server VM by JetBrains s.r.o.
Toolkit: sun.lwawt.macosx.LWCToolkit
macOS 14.6.1
GC: G1 Young Generation, G1 Concurrent GC, G1 Old Generation
Memory: 4096M
Cores: 12
Metal Rendering is ON
Registry:
 debugger.new.tool.window.layout=true
 ide.experimental.ui=true
 i18n.locale=
 python.debugger.use.dispatcher=true
Non-Bundled Plugins:
 me.lensvol.blackconnect (0.6.2)
 com.jetbrains.space (243.21565.122)
 org.jetbrains.plugins.gitlab (243.21565.204)

The issue is that when matplotlib > 3.8.4, this statement

import tkinter

 when executed in python 3.12 throws this error:

 File "~/.pyenv/versions/3.12.1/lib/python3.12/tkinter/__init__.py", line 38, in <module>

   import _tkinter # If this fails your Python may not be configured for Tk

   ^^^^^^^^^^^^^^^

ModuleNotFoundError: No module named ‘_tkinter’

However, it appears to be installed, as per the output of

brew install python-tk@3.12

==> Downloading https://formulae.brew.sh/api/formula.jws.json

################################################################################################################################## 100.0%

==> Downloading https://formulae.brew.sh/api/cask.jws.json

################################################################################################################################## 100.0%

Warning: python-tk@3.12 3.12.8 is already installed and up-to-date.

To reinstall 3.12.8, run:

  brew reinstall python-tk@3.12

What is the missing configuration that will connect the dots here?