Web Video Caster has worked best for me. For mirroring, I just use Google Home.
From an android phone.
Can understand what u exactly mean... but for casting I just normally go to specific app and click on cast button just like in yt app prime video, Disney + and many other local apps work the same. Also I don't use much but I have a Google TV app too which suggests the shows and starts directly on tv
Soul browser, VLC, bubble upnp
To do what you are asking, you must get a Chromecast. I don’t see any other way around it. Any software solutions would probably not be any more efficient than what you are already doing. If you have a spare HDMI spot, then pick up a Chromecast for that specific purpose. It doesn’t have to be the Google TV one. The original one should still work or get the second generation if you are worried about updates (I think update support is still available for that one.). If it’s 4K streams you are watching, then get the Chromecast Ultra. Otherwise unless the Roku has a decent web browser you could use or the Android box you are using can side load a web browser that you would be comfortable using, you might already have the best solution for you.
Web Video Cast is the way to go. Even if your TV or streaming device has built-in Chromecast, you should install the Web Video Caster Receiver app on there for better compatibility.
Or you can go on your phone what's the video for about 2 seconds then install the YouTube app on your device that's hooked to your TV and go to your history once you've logged into the YouTube app on your TV and boom there it is easy peasy
For web... Web video caster is the best imo