I ordered the capture card and the converter cable, and they should be here on Sunday. I'll try it and see how that goes before looking into any other options.
-wraith808
Keen to hear how well it works. Including which Android app to use - there are a few in the in Google Play and some appear to show ads.
-Nod5
So it worked quite well, with negligible perceived lag!

The cable connection- the HDMI from the Pi is at the bottom, then the capture card, then the adapter (used micro usb as that's what my old Samsung tablet has)

So when I first connected it, it asked if I wanted to open the app, and had a tick for always perform this action, which I did not tick. After that, a dialog warning to safely disconnect came up. I went ahead and connected- bad choice. As soon as I connected, I couldn't click the dialog as its over the display area. I had to reboot and try again, clicking the dialog before I connected the Pi. It comes up not in full screen, but if you tap the display, it expands. Tap it again to unexpand.

The Pi fullscreen.

A closer view of the screen.
I used USB Camera Pro - Connect EasyCap or USB WebCam (
https://play.google....p;hl=en_US&gl=US). They have a free version with ads, but with the refund policy on the play store, I figured I'd just go with the regular one, see if it worked, and if so keep it. Better than even starting out with ads as it was only $5.49US.
micro usb to HDMI -
https://smile.amazon.../product/B00LN3LQKQ/capture card -
https://smile.amazon.../product/B08CH9FC22/usb-c to HDMI -
https://smile.amazon.../product/B072V9CNTK/The capture card appears to be out of stock right now

This looks like the same one -
https://smile.amazon.com/dp/B08CXMLZCY/. It's about $5USD more than I paid though.