One home Xbox S with 2 different profiles have to share game progress, why?

Make sure to sign out the other account instead of just swapping the accounts.

It's still an easy fix, just a little different. Just log in with son 1's account on son 2's Xbox, and make the console the home Xbox. That will then let Son 2 use son 1's Gold with no extra cost. It just means that Son 1 has to be logged into Xbox Live
all the time on his console to be able to play his games. There is also no such thing as family share. That is why you have to set up the home console to share games and subscriptions.

You can achieve game sharing in 2 way.

All account can use Xbox Live and Game Pass on the Home console of the account that have active subscriptions.

Another way is to set an Xbox different from the one used by the account that have active subscriptions as home, in this way the other account(s) on this home console can use Xbox Live and Game Pass, and the account that have the subsciptions can always
use it in any console if is signed online.

But this works for 2 console at the same time, I think there is no way to gameshare on 3 console.

You would only be able to play it on 2 of the consoles with 2 different profiles at the same time the 3rd console would have to get its own copy of the game and its own gold subscription in order to play online multiplayer.

Here is a link that talks about home sharing

https://support.xbox.com/en-US/xbox-one/xbox-live/xbox-live-gold-sharing-features

Here is a link that explains how to set it up.

https://support.xbox.com/en-US/games/game-setup/my-home-xbox

If you are trying to do it on the same profile, then that is not possible. Profiles on Xbox One & Series X|S can only play games on one console at a time.

If you are trying to let someone else play your Game Pass games on a different console at the same time as you, then you need to make the console that you want to share the games on the Home Xbox using the account that has Game Pass, then anyone with a different profile can play those games at the same time as you.

Bear in mind the Home Xbox setting is only meant to be used in the same household, as using it with someone else not in your household can result in a suspension or ban.