I asked them and they just suggested restoring a backup which is not a good option in an online store.
I have manually copied the installation files across via ftp for front end and back end but that did not help.
Anything I should suggest to the host?
They gave you a predefined reply without checking anything in the server.
Even If something went wrong during the update you should have a different status code from the server, not a gateway timeout. They have the key to know what's happening as they have access to server logs...
Is the entire website (frontend and backend) showing the error?
The entire website was showing the error (front and backend) - so I just restored the backup and it's up again.
Will do a full backup and try the update again tomorrow and let you know how it goes.