As of 6/4/21 with OS10.0.0-4195 and RokuCast 1.9.6 and AirPlay2 1.14.104, screen mirroring is now working with Composite output on the 3910 for both Miracast & AirPlay2 based connections.
Previously (all previous firmware/app versions) composite output was excluded/non-functional when mirroring (RokuCast/AirPlay2 would close to home upon connecting):
https://support.roku.com/article/208754928
Does my Roku device support screen mirroring?
Most current generation Roku streaming players and Roku TVs support screen mirroring with notable exceptions listed below. To find the model of your Roku device, go to Settings > System > About.
As of 6/4/21 this information is no longer accurate/true, and mirroring (Miracast and AirPlay2) now works in composite output mode.
"As of 6/4/21 this information is no longer accurate/true, and mirroring (Miracast and AirPlay2) now works in composite output mode."
Is this still the case with the latest version of Roku OS in 2024?
Yes - AirPlay2 & Miracast mirroring both still work when connected in Composite (RCA) output mode with RokuOS 12.5.5-4174. This information comes from the OP.