Besides '.py', files with '.pyw' (Windows), '.pyi' (typing stub files), and no extension (especially *nix) may be Python files. Before #89610, IDLE was generallly restricted to '.py' and '.pyw' (mostly).

• Support open, highlight, and save for .pyi stub files.
  Make IDLE recognize .pyi stub files as source for open, save, and edit #89610
• Support browsing .pyw files and anything similar added in the future.
  IDLE: Browse non-.py python files #95411
• Support browsing .pyi files. Would this be useful?
• Support browsing no-extension files. Check current code.
• Support 'Open Module' for non-.py files. (Extra issue here is different extensions with same name.)

Interaction with OS

• Support double click of .pyi on macOS to edit in IDLE.
  gh-89610: Add .pyi as a recognised extension for IDLE on macOS #95393
• Support double click of any Python file on Windows to edit in IDLE. Currently, one may run with python or edit with Notepad or 'open' with another apps either listed or found by browsing. (Likely difficult.)
• Support right click on .pyi on Windows to Edit with IDLE. See Zoomba's response on Make IDLE recognize .pyi stub files as source for open, save, and edit #89610 (difficult).