So you would need to apply separately for EU261 on ba.com if you haven't already done so. It won't come through automatically.
You won't get any additional gesture if EU261 is payable - and there are some people saying they're waiting many weeks to hear back, but you should get your train fare back plus EU261 if BA believes it's payable. You may need to push for EU261 and you may get pushed back a few times on that - see the other thread on this.
The 2021/22 BA compensation thread: Your guide to Regulation EC261/2004
Was there any reason given for the domestic cancellation?