Ta1020
Certain apps on Roku devices have built-in Dial Support. (youtube, netflix).
This allows you to natively use the Cast feature on your Android mobile device/phone.
https://www.howtogeek.com/215791/use-your-tvs-hidden-dial-feature-to-cast-netflix-and-youtube-without-a-chromecast/
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For all the other channels/apps that do not have such capability (pluto, plex, hulu, tubi), you will need to "Screen Mirror" these apps so that you can use your Cast button. You can see from Roku Support article which Screen Mirroring protocols are supported by Roku on Android devices.
https://support.roku.com/article/208754928 - After reading the Android section, scroll down to the "Does my Android device support screen mirroring?" section.
Of all the Android phones I have used with my Roku devices, only my Umidigi F3, which has a "Wireless Display" setting that must be enabled in the Cast settings, has been able to cast everything to the Roku through Screen Mirroring. (ie. using the Cast icon/button).
As such, will need to see if any of the the listed supported protocols in the support article can be enabled on your phone to screen mirror/cast.
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An alternative to the screen mirroring option would be to use a third party casting app like Web Video Caster (WVC) or Castify which comes equipped with a browser that allows you to cast web content to the Roku device. (Both have free versions which work well and the paid versions unlock some "full" features like Bookmarks, etc).
The above casting apps are both available in the Play Store, and they require a companion receiver to be installed on the Roku device. (both receivers available in Roku Streaming/Channel Store).
Of the two, I prefer WVC (which offers a one-time, lifetime purchase for $5, but the free version works just fine). These casting apps can help you stream content through your Roku that may not be available via any channel/app.