Note: Next time, execute the commands one by one and when pasting the output, leave separations between the command because it’s a pain to read it 
(this time I’ve fixed it in your post).
Did you install roundcube using apt?
dpkg -l 'roundcube*' | grep ^ii
If you see that roundcube is installed you should remove it and reinstall it using Hestia script, to do it, follow these steps:
If roundcube was not installed using distro packages, check whether the db exists:
mysql -uroot -e 'use roundcube; show tables;'
If you can see the tables, then maybe the password being used in roundcube conf is not the same as for roundcube user in the db.
Check what is the password being used by roundcube:
grep db_dsnw /etc/roundcube/config.inc.php
And you should see an output like this:
$config["db_dsnw"] = "mysql://roundcube:abc123ABC34501yz@localhost/roundcube";
Where abc123ABC34501yz would be the password used so try to modify it for the db user:
mysql -uroot -e 'ALTER USER "roundcube"@"localhost" IDENTIFIED BY "abc123ABC34501yz"; flush privileges;'
Change roundcube dir perms:
chown -R hestiamail:www-data /etc/roundcube/
find /etc/roundcube/ -type f -iname "*php" -exec chmod 640 {} \;
chown -R hestiamail:www-data /var/lib/roundcube/
chown -R hestiamail:www-data /var/log/roundcube/
And try to connect to webmail again.