Wow, nice amp! Lots of switching functionality. Ideal for integrating to a home automation setup. You certainly should persist in getting it integrated.
Had a quick look at the manual and also the service manual. Impressed that there is a full disclosure of control codes, circuit diagrams and even chip numbers. Kudos to Arcam. This is how all manuals should come, with full details.
Your amp uses an industry standard MAX232 interface chip for the serial interface, and the parameters needed are as you described. 38400 81n.
Have you connected your USB device to a Windows machine and the amp to check if a firmware update is required for the amp? That can also be used to confirm your USB Adapter and cable is correctly configured and working. Use a serial terminal program such as PuTTY, and the amp should respond to commands with an ok or error code as mentioned in the appendix at the end of the user manual pertaining to serial control. As a quick check your USB serial adapter FTDI UART is working, short pin 2 and 3 on the RS232 connector and the screen should respond with an echo of what you type there, either one or two characters, depending if you turned echo on or off in your terminal program. Once we are confident the serial port is working, we can check other things.
Some cheaper USB adapters only swing 0 to +5volts, not +/-12volts like the RS232 standard dictates. This may be the source of your woes. Measure the voltage on both pin 3 and pin 2 to pin 5 (Ground) on your USB RS232 adapter with a multimeter set to 12volts or more DC range. Are they minus 12 volts for either in respect to pin 5 (Ground)? If so, you have true RS232. If not, you may need alternative measures we can discuss later. Check also at your amp.
Please report back on all four readings if you have a multimeter.
Some RS232 cables are straight through Tx to Tx, Rx to Rx. Others swap them so the send goes to receive. This may also be a source of trouble if it is not correct. A common gotcha, easily checked by swapping them and seeing if it then works. You won’t blow up anything if you get it wrong. You can also check with your multimeter if pin 2 on one end goes to pin 2 or pin 3 on the other end of the cable.
Can you include a picture of your RS232 adapter or the URL to where you bought it from? The cable also? Side as well as connector end on. Is there a chip on the USB adapter the has the number 232 on it. If so, what are the rest of the alphanumeric characters on that chip?
I note the Infrared model CR80 remote control for the AVR250 is based on the common Philips RC-5 standard. The main system control uses RC-5 system codes ‘16’, and also ‘17’. This may also be another avenue to control your amp. The RS232 gives you full control, but infrared may be sufficient for daily needs. ESPHome has recently added IR support.
Another option may be ESPHome with a ESP32 and a RS3232 voltage translator to match the correct voltages to speak directly to your AVR250 amp. The benefits are you can control UART traffic both ways, decode strings and error codes in a controlled way as well, which you can’t do with a ESP32 and IR.
The final option is to use a Python serial library and write your own integration. You may use another integration as your starting template and modify it for your own use. Stand on the shoulder of giants.