If you want to be online, but want to block internet to certain apps like work apps, messaging apps etc, and continue using rest of your apps, you can do it using this app.
And no,this is not an ad. https://play.google.com/store/apps/details?id=dev.tuantv.android.netblocker
You should be able to go into App Info>Mobile Data & Wifi and disable network access without installing anything on the latest versions of Android if I am not mistaken.
You can also use apps like Shelter to create work and personal profiles if you want to cleanly separate the two.
I can only disable background network access using this method. Android 13 Pixel phone
Shelter and Island are good options for creating separate work profiles. But disabling internet per app feature is not present in all roms. So for those who are not having it could use this.
@CorrodedCranium
Generally speaking, thats a feature projects like LineageOS or GrapheneOS add, but it never made it upstream into AOSP.