If you don't want to reformat your NTFS drive, the best way to write to it on a Mac is by using third-party NTFS for Mac software. I use iBoysoft NTFS for Mac on my Intel MacBook Air running macOS Ventura.
It is by far the best I've seen. I tested several NTFS for Mac software that I found in this NTFS for Mac roundup and decided to continue with iBoysoft NTFS for Mac. It's super easy to use after being installed. I don't need to reopen the app after reconnecting my NTFS drive or rebooting my Mac. It just works seamlessly on my Mac, like a native macOS drive.
According to its official website, it supports macOS 13 Ventura ~ macOS 10.13 High Sierra on Intel-based, M1, and M2 Macs. BTW, it also enables you to write to a Boot Camp NTFS partition, unmount, and check & repair your NTFS drive.
You can test its free trial to see if it's what you need.
Here's a tutorial for writing to NTFS drives on Mac: