No. You can give your email and it enables some additional functionality such as iCloud if you want to opt in to that but it’s not required.
When it asks if you have an Apple ID (which can be any email address) there is a skip button in very plain language on a very uncluttered screen where it is very easy to read.
And no, it never asks for a phone number. You are free to add one later though if you choose. But the OS doesn’t want it or use it...
The only place I can think of where you can put in your phone number is the Messages app, which is not even part of the OS.
You would do this on your own initiative by the way, not requested by the app or by the OS. Putting your number into that allows SMS messages to appear on your computer.
When it asks if you have an Apple ID (which can be any email address) there is a skip button in very plain language on a very uncluttered screen where it is very easy to read.
And no, it never asks for a phone number. You are free to add one later though if you choose. But the OS doesn’t want it or use it...
The only place I can think of where you can put in your phone number is the Messages app, which is not even part of the OS.
You would do this on your own initiative by the way, not requested by the app or by the OS. Putting your number into that allows SMS messages to appear on your computer.