Here's how to change the way the Twitter app handles videos nested in new tweets (Video Auto-Play). You can indeed configure the Twitter app to automatically play videos when your smartphone is connected to Wi-Fi only if you don't want the app to tap into your mobile data or permanently turn off video Auto-Play.
Open the Twitter app, tap on the Menu > Settings. Go to GeneralSettings > Video Auto-Play:
Three options are available: Use mobile data and Wi-Fi, Use Wi-Fi Only and finally Never play videos automatically:
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