You were using the free WiFi in the airport not the navigator lounge WiFi which they give a password for.

the reason this is done is not BA. Russian Law requires a person using (public) WiFi to be identified unless it’s a private WiFi. Navigator is private and requires no password, airport WiFi is public and therefore an ID is needed.

this has been the case for a number of years and all public WiFi now requires this.

there is a second option you must have missed which is the SMS option where you enter your number and receive an SMS. Most Russians don’t use this as the call cost is basically zero to them, hence why the call
option is presented first.