If your storing millions of passwords surely a version field and an if statement is not going to be a huge concern
https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpubli...
If you're actually using a 'strong enough' hash to prevent easy cracking if your hashed password database is leaked then you're doubling the server load which can be quite substantial in some cases.
And obviously this is server side