Acronis Cyber Infrastructure: registration of Backup Gateway under user with two-factor authentication fails

Symptoms

You want to use Acronis Cyber Infrastructure Backup Gateway to connect storage backend to Acronis Cyber Cloud. You have two-factor authentication (2FA) enabled for the cloud tenant where you want to register this storage and this tenant's users.

Manual ACI Backup Gateway registration in Acronis Cyber Cloud per Backup Gateway Quick Start Guide fails with the following error in UI: