That is what I am going to do, getting a Chromecast. My question now is, how to I make the phone talk to the Chromecast??
That’s up to you to figure out. This is a Roku community. Not a Chromecast community. But since you have an old phone it may not even work. Best bet is to do some research. I’m sure people aren’t in the Chromecast community asking “How do I do this on my Roku”.
I have an iPhone 13 Pro running iOS 15.3.1. I can stream music from my phone to my Roku using Apple AirPlay. I can also mirror my phones screen to my Roku. My son can mirror his Galaxy S21 Plus to his Roku with no issues. It’s running Android version 12. This is using a Roku Streaming Stick 4K or my TCL Roku TV. Each is running Roku OS 10.5
Assuming they are both on the same network, you wont have to do much:
1) To mirror, you should simply be able to use the phone's "Cast" function/Google Home app that you mentioned before, and select your new GC/CC-compastible device.
2) To cast, simply use the Cast icon within each app and select your new GC/CC-compatible device.