I am confused because as you can see in this screenshot, when putting in an A record for the www. route, it wants me to put in an ipv4 address for the website (which I don't know) , whereas for the CNAME it needed that 'jaixxbni...' content string. Please help.

I'm sorry I don't quite understand is the issue that you're saying the old domain pop up in Google

Or is the issue that there is a URL string somewhere that's redirecting to somewhere else? Can you provide a link?

The issue is that this link (https://ymgmovement.org.au/) isn't the one that pops up in google. The link that comes up in Google is https://www.ymgmovement.org.au ... but that link doesn't work. I'd like to get rid of that old link from google and put the new one in that is deployed with Railway.

Look at this screenshot here, I'm trying to add a redirect in Cloudflare from https://www.ymgmovement.org.au to https://ymgmovement.org.au but it's asking me to first create a new proxied DNS record and I need the IPv4 address, so how exactly do I do that? For the other CNAME DNS Railway just gave me a target Url jaixnbni.up.railway.app ... so what's the IPv4 address so I can do this? If you have any other solutions that would work too great - Thanks!

You can use Google's Search Console to request URL removal for the old domain. Additionally, updating the sitemap to reflect the new domain will help Google index the correct link. Please note that Railway doesn't control Google's behavior in search results.