pre-commit: Executable python not found when committing a new file - virtualenv

Question

I'm trying to use pre-commit 2.20.0 on Ubuntu 22.04.1 / Python 3.10.6.
I followed the instructions at https://pre-commit.com/#installation and installed pre-commit with pip (22.2.2).
Here's my .pre-commit-config.yaml file:
$ cat /home/username/Projects/web/app/.pre-commit-config.yaml
default_language_version:
python: python3.10
repos:
- repo: https://github.com/pycqa/isort
rev: "5.10.1"
hooks:
- id: isort
args: ["--profile", "black"]
- repo: https://github.com/psf/black
rev: "22.8.0"
hooks:
- id: black
language_version: python3.10
But I face an error when committing a new file:
$ git commit -m "Update file."
[INFO] Installing environment for https://github.com/pre-commit/pre-commit-hooks.
[INFO] Once installed this environment will be reused.
[INFO] This may take a few minutes...
An unexpected error has occurred: CalledProcessError: command: ('python', '-mpip', 'install', '.')
return code: 1
expected return code: 0
stdout:
Executable `python` not found
stderr: (none)
Check the log at /home/username/.cache/pre-commit/pre-commit.log
The same error occurs when using a virtual environment (virtualenv 20.16.5):
$ virtualenv venv
created virtual environment CPython3.10.6.final.0-64 in 170ms
creator CPython3Posix(dest=/home/username/Projects/web/app/venv, clear=False, no_vcs_ignore=False, global=False)
seeder FromAppData(download=False, pip=bundle, setuptools=bundle, wheel=bundle, via=copy, app_data_dir=/home/username/.local/share/virtualenv)
added seed packages: pip==22.2.2, setuptools==65.3.0, wheel==0.37.1
activators BashActivator,CShellActivator,FishActivator,NushellActivator,PowerShellActivator,PythonActivator
$ git commit -m "Update file."
[INFO] Installing environment for https://github.com/pre-commit/pre-commit-hooks.
[INFO] Once installed this environment will be reused.
[INFO] This may take a few minutes...
An unexpected error has occurred: CalledProcessError: command: ('python', '-mpip', 'install', '.')
return code: 1
expected return code: 0
stdout:
Executable `python` not found
stderr: (none)
Check the log at /home/username/.cache/pre-commit/pre-commit.log
Here's the full log:
$ cat /home/username/.cache/pre-commit/pre-commit.log
pre-commit version: 2.20.0
git --version: git version 2.34.1
sys.version:
3.10.6 (main, Aug 10 2022, 11:40:04) [GCC 11.3.0]
sys.executable: /usr/bin/python3
os.name: posix
sys.platform: linux
### error information is the same as here above
Traceback (most recent call last):
File "/usr/local/lib/python3.10/dist-packages/pre_commit/error_handler.py", line 73, in error_handler
yield
File "/usr/local/lib/python3.10/dist-packages/pre_commit/main.py", line 358, in main
return hook_impl(
File "/usr/local/lib/python3.10/dist-packages/pre_commit/commands/hook_impl.py", line 254, in hook_impl
return retv | run(config, store, ns)
File "/usr/local/lib/python3.10/dist-packages/pre_commit/commands/run.py", line 424, in run
install_hook_envs(to_install, store)
File "/usr/local/lib/python3.10/dist-packages/pre_commit/repository.py", line 223, in install_hook_envs
_hook_install(hook)
File "/usr/local/lib/python3.10/dist-packages/pre_commit/repository.py", line 79, in _hook_install
lang.install_environment(
File "/usr/local/lib/python3.10/dist-packages/pre_commit/languages/python.py", line 221, in install_environment
helpers.run_setup_cmd(prefix, install_cmd)
File "/usr/local/lib/python3.10/dist-packages/pre_commit/languages/helpers.py", line 48, in run_setup_cmd
cmd_output_b(*cmd, cwd=prefix.prefix_dir, **kwargs)
File "/usr/local/lib/python3.10/dist-packages/pre_commit/util.py", line 146, in cmd_output_b
raise CalledProcessError(returncode, cmd, retcode, stdout_b, stderr_b)
pre_commit.util.CalledProcessError: command: ('python', '-mpip', 'install', '.')
return code: 1
expected return code: 0
stdout:
Executable `python` not found
stderr: (none)
Here is my venv/ folder structure:
$ tree -L 3 venv/
venv/
├── lib
│   └── python3.10
├── local
│   ├── bin
│   │   ├── activate
│   │   ├── activate.csh
│   │   ├── activate.fish
│   │   ├── activate.nu
│   │   ├── activate.ps1
│   │   ├── activate_this.py
│   │   ├── deactivate.nu
│   │   ├── pip
│   │   ├── pip3
│   │   ├── pip-3.10
│   │   ├── pip3.10
│   │   ├── python -> /usr/bin/python3
│   │   ├── python3 -> python
│   │   ├── python3.10 -> python
│   │   ├── wheel
│   │   ├── wheel3
│   │   ├── wheel-3.10
│   │   └── wheel3.10
│   └── lib
│   └── python3.10
└── pyvenv.cfg
6 directories, 19 files
...which may be the cause of the trouble as per https://github.com/pypa/virtualenv/issues/2350 but I can definitely not understand all the story.
More:
$ which python # empty result!
$ which python3
/usr/bin/python3
$ ls -l /usr/bin/python3
(...) /usr/bin/python3 -> python3.10
Did I miss something in the pre-commit installation?
How could I properly and simply (#basic user) fix this error, if possible?