現在の問題

$ sudo apt upgrade

You might want to run 'apt --fix-broken install' to correct these.
The following packages have unmet dependencies:
 libpython3.12 : Depends: libpython3.12-stdlib (= 3.12.9-1+focal1) but 3.12.7-1+focal1 is installed
 libpython3.12-dev : Depends: libpython3.12-stdlib (= 3.12.9-1+focal1) but 3.12.7-1+focal1 is installed
 python3.12-dev : Depends: python3.12 (= 3.12.9-1+focal1) but 3.12.7-1+focal1 is installed
 python3.12-venv : Depends: python3.12 (= 3.12.9-1+focal1) but 3.12.7-1+focal1 is installed
E: Unmet dependencies. Try 'apt --fix-broken install' with no packages (or specify a solution).

apt upgradeを実施すると、Pythonの依存関係のエラーが発生する。
エラーを読んでみると、どうやらインストールされているPython関連のパッケージと要求バージョンが一致しない模様

インストール済みバージョン：3.12.7-1+focal1
要求されるバージョン：3.12.9-1+focal1

提示された自動修正のコマンドを実行

$ apt --fix-broken install

Preparing to unpack .../python3.12_3.12.9-1+focal1_amd64.deb ...
Unpacking python3.12 (3.12.9-1+focal1) over (3.12.7-1+focal1) ...
dpkg: error processing archive /var/cache/apt/archives/python3.12_3.12.9-1+focal1_amd64.deb (--unpack):
 trying to overwrite '/usr/bin/python3.12', which is also in package python3.12-minimal 3.12.7-1+focal1
dpkg-deb: error: paste subprocess was killed by signal (Broken pipe)
Preparing to unpack .../libpython3.12-stdlib_3.12.9-1+focal1_amd64.deb ...
Unpacking libpython3.12-stdlib:amd64 (3.12.9-1+focal1) over (3.12.7-1+focal1) ...
dpkg: error processing archive /var/cache/apt/archives/libpython3.12-stdlib_3.12.9-1+focal1_amd64.deb (--unpack):
 trying to overwrite '/etc/python3.12/sitecustomize.py', which is also in package libpython3.12-minimal:amd64 3.12.7-1+focal1
dpkg-deb: error: paste subprocess was killed by signal (Broken pipe)
Errors were encountered while processing:
 /var/cache/apt/archives/python3.12_3.12.9-1+focal1_amd64.deb
 /var/cache/apt/archives/libpython3.12-stdlib_3.12.9-1+focal1_amd64.deb
E: Sub-process /usr/bin/dpkg returned an error code (1)

依存関係は修正されず、エラーが続く。

上記で、同様のエラーの解決方法を記載されていたので、同じ手順でやってみる。（これでは解決しませんでした）

Python 3.12関連のパッケージ確認

$ dpkg -l |grep python3.12

iU  libpython3.12:amd64               3.12.9-1+focal1                   amd64        Shared Python runtime library (version 3.12)
iU  libpython3.12-dev:amd64           3.12.9-1+focal1                   amd64        Header files and a static library for Python (v3.12)
ii  libpython3.12-minimal:amd64       3.12.7-1+focal1                   amd64        Minimal subset of the Python language (version 3.12)
ii  libpython3.12-stdlib:amd64        3.12.7-1+focal1                   amd64        Interactive high-level object-oriented language (standard library, version 3.12)
ii  postgresql-plpython3-12           12.22-0ubuntu0.20.04.2            amd64        PL/Python 3 procedural language for PostgreSQL 12
ii  python3.12                        3.12.7-1+focal1                   amd64        Interactive high-level object-oriented language (version 3.12)
iU  python3.12-dev                    3.12.9-1+focal1                   amd64        Header files and a static library for Python (v3.12)
ii  python3.12-minimal                3.12.7-1+focal1                   amd64        Minimal subset of the Python language (version 3.12)
iU  python3.12-venv                   3.12.9-1+focal1                   amd64        Interactive high-level object-oriented language (pyvenv binary, version 3.12)

確かに、バージョン不一致が確認できますね。

パッケージの詳細確認

$ apt show python3.12 python3.12-minimal
~~
APT-Sources: http://ppa.launchpad.net/deadsnakes/ppa/ubuntu focal/main amd64 Packages

参考にしたQiitaの記事と同様に、deadsnakeという（ディストリビューション？）のPythonバージョンが入っていた。

依存関係を確認

$ apt rdepends python3.12 python3.12-minimal

python3.12
Reverse Depends:
  Depends: libpython3.12-testsuite (>= 3.12.9-1+focal1)
  Recommends: python3.12-minimal
  Depends: python3.12-venv (= 3.12.9-1+focal1)
  Depends: python3.12-tk
  Depends: python3.12-gdbm
  Depends: python3.12-full (= 3.12.9-1+focal1)
  Depends: python3.12-examples (>= 3.12.8-1+focal1)
  Depends: python3.12-examples (>= 3.12.9-1+focal1)
  Depends: python3.12-dev (= 3.12.9-1+focal1)
  Depends: python3.12-dbg (= 3.12.9-1+focal1)
  Depends: libpython3.12-testsuite (>= 3.12.8-1+focal1)
  Depends: idle-python3.12
  Enhances: idle-python3.12
  Depends: idle-python3.12
  Enhances: idle-python3.12
python3.12-minimal
Reverse Depends:
  Depends: python3.12 (= 3.12.7-1+focal1)

$ apt rdepends libpython3.12-minimal libpython3.12-stdlib libpython3.12-minimal

libpython3.12-minimal
Reverse Depends:
  Depends: libpython3.12-stdlib (= 3.12.7-1+focal1)
  Depends: python3.12-minimal (= 3.12.7-1+focal1)
libpython3.12-stdlib
Reverse Depends:
  Depends: python3.12 (= 3.12.7-1+focal1)
  Depends: libpython3.12 (= 3.12.9-1+focal1)
  Recommends: libpython3.12-minimal
  Depends: python3.12 (= 3.12.9-1+focal1)
  Depends: libpython3.12-dev (= 3.12.9-1+focal1)
  Depends: libpython3.12-dbg (= 3.12.9-1+focal1)
libpython3.12-minimal
Reverse Depends:
  Depends: libpython3.12-stdlib (= 3.12.7-1+focal1)
  Depends: python3.12-minimal (= 3.12.7-1+focal1)

Pythonの依存関係があるパッケージを削除

参考にした記事の通り、依存関係が発生しているPythonパッケージを削除

$ sudo apt remove python3.12-minimal libpython3.12-minimal

Reading package lists... Done
Building dependency tree       
Reading state information... Done
You might want to run 'apt --fix-broken install' to correct these.
The following packages have unmet dependencies:
 libpython3.12 : Depends: libpython3.12-stdlib (= 3.12.9-1+focal1) but 3.12.7-1+focal1 is to be installed
 libpython3.12-dev : Depends: libpython3.12-stdlib (= 3.12.9-1+focal1) but 3.12.7-1+focal1 is to be installed
 libpython3.12-stdlib : Depends: libpython3.12-minimal (= 3.12.7-1+focal1) but it is not going to be installed
 python3.12 : Depends: python3.12-minimal (= 3.12.7-1+focal1) but it is not going to be installed
 python3.12-dev : Depends: python3.12 (= 3.12.9-1+focal1) but 3.12.7-1+focal1 is to be installed
 python3.12-venv : Depends: python3.12 (= 3.12.9-1+focal1) but 3.12.7-1+focal1 is to be installed
E: Unmet dependencies. Try 'apt --fix-broken install' with no packages (or specify a solution).

ここも、依存関係が発生してしまっていて解決できない。

解決方法

最終手段、Pythonパッケージを削除します。

postgresql-plpython3-12 以外を削除対象とします。これは PostgreSQL の拡張機能であり、Python 3.12 に直接依存しない可能性があるためです。

Ubuntuにデフォルトで入ってるPythonは、システムと依存関係がある場合が大いにあります。
事前に十分にご確認ください。

関連のパッケージ削除

ご自身の依存関係に合わせて削除してください。

$ sudo apt purge libpython3.12:amd64 libpython3.12-dev:amd64 libpython3.12-minimal:amd64 libpython3.12-stdlib:amd64 python3.12 python3.12-dev python3.12-minimal python3.12-venv

依存関係の修復・不要なパッケージ削除

sudo apt --fix-broken install
sudo apt autoremove

Pythonを再インストール

sudo apt install python3.12 python3.12-dev python3.12-venv libpython3.12-dev

解決。