Can't remotely connect to my postgresql database on digitalocean

Question

I'm trying to connect to my postgres db located on a digitalocean's droplet using psycopg2 package.

However, I keep getting this error message :

psycopg2.OperationalError: connection to server at "***.***.***.***", port 5432 failed: Connection timed out (0x0000274C/10060)
   Is the server running on that host and accepting TCP/IP connections?

I've made all the necessary modifications to both postgresql.conf and pg_hba.conf files, and restarted postgresql service.

#postgresql.conf
listen_addresses = '*' #both were uncommented 
port = 5432

#pg_hba.conf
host      all       all      0.0.0.0/0      md5
host      all       all      ::/0           md5
hostssl   all       all      0.0.0.0/0      md5   #tried with and without this line

When I run service postgresql status I see that my service is active.

And when I run netstat -na I get the following :

Proto Recv-Q Send-Q Local Address           Foreign Address         State      
tcp        0      0 127.0.0.54:53           0.0.0.0:*               LISTEN     
tcp        0      0 127.0.0.53:53           0.0.0.0:*               LISTEN     
tcp6       0      0 :::80                   :::*                    LISTEN     
tcp6       0      0 :::22                   :::*                    LISTEN 

It looks like port 5432 is not open. I also tried using sudo ufw allow 5432/tcp but it didn't change anything.

Do you have any idea what I'm doing wrong ?

EDIT (to answer @Adrian Klaver's question) :

1. I run netstat -na both in root and postgres.
2. sudo ufw status return the following :

To                         Action      From
--                         ------      ----
Apache                     ALLOW       Anywhere                  
OpenSSH                    ALLOW       Anywhere                  
5432/tcp                   ALLOW       Anywhere                  
Apache (v6)                ALLOW       Anywhere (v6)             
OpenSSH (v6)               ALLOW       Anywhere (v6)             
5432/tcp (v6)              ALLOW       Anywhere (v6) 

3. ps ax | grep postgres returns the following :

 9320 pts/0    S+     0:00 sudo -u postgres psql
   9321 pts/1    Ss     0:00 sudo -u postgres psql
   9322 pts/1    S+     0:00 /usr/lib/postgresql/15/bin/psql
   9721 pts/2    S+     0:00 sudo -i -u postgres
   9722 pts/3    Ss     0:00 sudo -i -u postgres
  10141 pts/5    S+     0:00 sudo -i -u postgres
  10142 pts/6    Ss     0:00 sudo -i -u postgres
  10234 pts/7    S+     0:00 grep --color=auto postgres

4. there's no external firewall