At least one controlled study supports this: (https://www.nature.com/articles/s41598-023-50354-3)

They had participants spend either 45 mins doing normal smartphone use or 45 minutes watching a documentary, and the results were that both increased mental fatigue but the documentary group did not have reduced cognitive function, whereas regular smartphone use did.

"Results suggested that both watching a documentary and using a smartphone for 45 min increased subjective mental fatigue and drowsiness. Watching the documentary did not impair cognitive performance. Reaction times on the PVT and number of errors on NoGo trials in the Go/NoGo task were higher among the participants in the smartphone condition. These results indicate reduced vigilance and impaired inhibition capacities only after smartphone use. "