System Information
Operating system: Windows 7
GPU: Radeon Vega 64, Divider version: 19.4.1
CPU: Intel Core i7-5960X

Blender Version

Broken: blender-2.80-f6cb5f54494e-windows64 (official release)
Broken: blender-2.81-115a5bf65a6b-windows64 (build bot)
Broken: blender-2.82-ba1e9ae4733a-windows64 (build bot)
Working: blender-2.79b-f4dc9f9d68b-windows64 (official release)

Short description of error

Since the drop-down menu for How to sync Playback got moved
into the Playback drop-down menu, its ability to be keyed got broken.

2.80 and onwards opens these keyed properties correctly
(from 2.97b and earlier), but does not allow any control over the
keyframe(s) from the context menu or keyboard shortcuts.

Exact steps for others to reproduce the error from scratch

• Open a broken version
• In the timeline editor --> Playback drop-down menu
• Over the How to sync Playback try inserting a keyframe (right-clicking or pressing I)