I've had a leak from a radiator which has badly stained the bedroom carpet. The CH system has been recently drained and refilled with water and corrosion inhibitor.
Your ideas are welcome.
The trouble can be when you drain the central heating system the "sludge" at the bottom of the radiator can be washed away, leaving small holes at the bottom of the radiator where it has rusted and these can leak.
This happened to me a few years ago.
You could replace the radiator and / or replace the carpet or both.
Can only suggest checking what specialised stain removers there are in the supermarkets and DIY sheds. I've given up on the stains on my carpet. Cleaners either do nothing or remove the carpet colour. I'm just putting up with them. Tend not to have visitors anyway.
The carpet is only 2yrs old and we really like it. The pattern is no longer manufactured & the Mrs got for a snip...£10-00/mt instead of £30-00/mt. We've claimed on the insurance & intend to put a new carpet down in the lounge with the money.