If you used that phone in the past with google services that's the reason it bypassed sms. When using a fresh android on a vpn and off a vpn, I've been prompted for phone numbers.
The best bypass not attaching to previous accounts or identities i found was creating on hotel or public networks. I was able to set up accounts for nvidia shields on hotel networks and bypassed the sms verification. After taken home they were placed on a subnet that only talks to the local server.
Every service I have come across has an option for a standard email and password. Although privacy wise I am not sure if that is any better than just signing in via Google. But most sites you can use a 10 minute mail email or similar if you aren't worried about getting locked out down the road.
No. Google has too much surveillance on the net. But if it helps, whatever they want to know, they already do. Creating that account won’t all of a sudden make them aware of your mysterious presence.
Dont use a VPN, dont use online SMS providers, dont use known altadress etc providers but things like a throwaway GMX account or so. Use a burner altadress for those.
Google "knows" many of the SMS providers simply because people use them exactly for that.
The thing is that Google accounts aren't only used for mail though; reliable access to the Play Store through Aurora, as well as access to paid apps, needs a Google account for instance