Interior Sliding Door Latch or Snib, openable from both sides

A router (along with a special guide) can be used to cut part of the inset you need, but is not the easiest tool to use if you are not experienced, and it does not cut square corners, which still require a chisel to finish.

Using a chisel does take care and practice, but it is not beyond the reach of even an amateur if you are willing to do a test piece first and then go very slowly.

You need to draw the opening with a sharp pencil (or and awl). Many people use a utility knife to cut the outline to slightly deeper than needed, then use a small, sharp chisel, following the grain of the wood (in this case toward the top and bottom, not across the door) taking very thin layers out until you are deep enough.

It does not need to be perfectly flat at the bottom of the channel, just the right depth at the ends with no high spots in between.

If you practice on a scrap of wood first, you may be surprised that you can do it.

My guess is the door has warped, touching the top or the bottom or both top and bottom of the door jam. If you remove that jam and reinstall it to follow the curvature of the door, when it is properly closed, that should fix the problem.