Accessing systray icons in the test suite is fragile

See #8928-note_26 & #8928-note_28

Feature Branch: kytv:bugfix/9258-systray-is-ready

Parent Task: #5330 (closed)

Related issues

• Related to #5632 (closed)
• Blocks #9095 (closed)

Original created by @kytv on 9258 (Redmine)