Use jammy ubuntu version, for install the PGAdmin on linux-mint.

1) Install the public key for the repository (if not done previously):

sudo curl https://www.pgadmin.org/static/packages_pgadmin_org.pub | sudo apt-key add

2) Create the repository configuration file: (jammy is important)

sudo sh -c 'echo "deb https://ftp.postgresql.org/pub/pgadmin/pgadmin4/apt/jammy pgadmin4 main" > /etc/apt/sources.list.d/pgadmin4.list && apt update

3) Install pgAdmin

sudo apt install pgadmin4

4) Install for desktop mode only

sudo apt install pgadmin4-desktop

5) If you need, also install for web mode only:

sudo apt install pgadmin4-web 

6) After install pgadmin4. Configure the webserver, (if you installed pgadmin4-web)

sudo /usr/pgadmin4/bin/setup-web.sh

Reference :

• https://stackoverflow.com/questions/68777587/linux-mint-20-x-ubuntu-based-cant-install-pgadmin4
• https://www.pgadmin.org/download/pgadmin-4-apt/