Well...
1) Samsung Galaxy S7 = my main phone, app still present from transfer from...
2) Samsung Galaxy S7 Edge, previous main phone that died. Repaired, now running Android 11+ as a Google Pixel 5. Tried everything suggested here, no joy at all. This was what prompted the thread.
3) Samsung Galaxy S5 Neo running LineageOS 15, Android 8.1. Went to Cyclechat using Chrome, logged in. Dropped the three dot menu at top right, lo and behold, Add to Home Screen. Tap. "Installing App". And sure enough, there it is.
I'm assuming the version of Chrome on the Samsung Pixel...wait one...I've just realised that on this device, Chrome actually says, "Install App" instead of Add to Home Screen! So I have !
So mystery solved so far as I am concerned, all Galaxies have the App!