Quote from a sibling comment:

  - macOS: Accessibility API
  - Windows: UI Automation
  - Linux: AT-SPI

The levels of support are radically different. Compositors, window managers, UI frameworks, and apps all have mixed and inconsistent levels of support such that the overall experience is that you simply cannot rely on using a Linux system via accessibility.

Unfortunately AT-SPI support is very hit or miss, mostly miss. To get it useable for this required a huge amount of modification. See my other comment for context.