I encountered a similar difficulty with playback stopping after each clip in the timeline. Did you check that the following box is unchecked in the "UI Settings" page of the "User" Tab of the Davinci Resolve "Preferences" Window:
"Stop Playback when a dropped frame is detected" ?
It stops when it encounters a new clip, for one second and then it goes further like elastic, the time line cursor shoots a few seconds further... Very annoying. Somebody can help? In 19.1.3. this problem was not there.