NTFS is proprietary FS that works on Linux thanks to great reverse-engineering efforts. To make this more fair, try accessing ext4 partition from Windows. Oh, it can’t even recognize it. Except that ext4 is open-source, so it wouldn’t even require reverse-engineering.
That said, have you fully shutdown Windows? You generally get write access out of the box nowadays, but only if Windows is fully shutdown. And clicking “Shut down” does not properly shut it down unless you disable fast startup.
Another method is to choose a “Restart” in Windows, and then instead of continuing with the restart, choose Linux on bootloader screen after you get there.