Wood around stove pipe
Depends on what the manufacturers specifications say.

For the particular doublewall insulated chimney (not "stovepipe" which is singlewall) I last had to work with, clearance to combustables was 2" from the pipe wall. The deformations at the joint appear to be consistent with what you have being double or triple wall insulated chimney, not stovepipe.

Stovepipe (singlewall) typically needs at least 18" clearance to combustibles, as it may get red-hot in the event of an excessive fire in the stove, or a chimney fire in the pipe.

Since the part shown is intended for framing support it's typically safe to have wood where the sheet screws in for support.

But the manufacturers specs (for the exact pipe and accessories you are actually working with) is what rules. You can almost certainly find out who that is by carefully examining the pipes (the info will be stamped into every piece, in my experience.) Then you should be able to look up the installation manual for the pipe and support piece.