I can't see the stitching on your photos (at least I can't see it on the screen of my phone, ) but I know that type of bar tape. I have not had the experience of removing (let alone reusing) it, but I'm sure it's worth a try. I did put leather similar to that on that old Drysdale I restored.

As ​​​nlerner suggests, get it good and wet, then carefully cut the stitching. Water should soften it up nicely.

Before you take it off, have your needle and thread ready. Take the leather off, take the brake lever off, change the stem, and get ready to put the leather back on. That's the tricky bit!

When you take it off, you have to put it back on before it dries out or loses its shape. Stitch up the whole tube, leaving the gap for the brake lever, without the handlebar. Leave the stitches very loose, like at least 1 cm extra thread on each stitch. Then slide it on, and slide the brake lever on in its place. Use more water as needed. When the leather is more or less where you want it, tighten the lever where it belongs. Now you start tightening up the thread, pull out the excess a little bit at a time while manipulating the leather back to where it was. Should be a fun project!

If the leather tears while you're getting it off, cut your losses. It may not be salvageable.

Good luck!