What's the best way to replace a failing boot drive?

Cloning is the direct route if you want to keep Windows, programs, settings and files together. Clonezilla or Rescuezilla can do it, and it's worth checking whether the new drive includes a cloning tool such as Acronis.

Double-check which disk is the source and which is the destination before starting. The destination will be overwritten. Once the clone is finished, try booting from the new drive, preferably with the old one disconnected.

I'd lean toward a clean Windows install instead. Disconnect the old drive while installing to the new one, then reconnect it and copy over the files you need. You'll have to reinstall your programs, but you won't be bringing a potentially damaged Windows installation along with them.

The failure changes the priority here. If there's anything irreplaceable and no backup, recover that first rather than starting with a full clone. Repeated reads can put more stress on a failing disk.

For a difficult drive, ddrescue on Linux is a recovery-oriented option for making a copy. If the data is valuable and the drive is getting worse, consider professional recovery rather than continuing to experiment with it.

If the replacement hasn't been chosen yet, consider an SSD for the boot drive. Even a basic SATA SSD can make Windows and apps feel much quicker than a spinning hard drive.