Those are huge software packages, with their own developers, with high code quality and testing standards.
I wish to make some small modifications to the code. Those modifications will probably not comply with the high code programming standards of the main branches, are probably not necessary for the mainstream developers, but I do need them.
Consider those changes as my own sandbox.
How can I create a version of those packages with my own changes without interfering with the main branches and complying with any code standards required by the official developers of those packages, or requiring any approvals for commits?
You might be interested in the GitHub Guide to forking a project. Forking allows you to create a copy of a repository which you can tinker around with on your own and if you do make changes which you think that the original project could benefit from, you can make a Pull Request. But it's also fine to fork a repository without intent to contribute if you want to learn from a particular project.