Earlier quoted context omitted.
I think it's likely the Elizabeth Line branch is suspended because the stations are closed, and the stations are closed because there's no power to the buildings.
The Elizabeth line is fully electrified, so why wouldn't the issue be power to the trains themselves rather than the stations?
National Rail say [1] "An unadvertised shuttle service is running from Heathrow Terminals to London Paddington to ensure customers and colleagues can leave the airport" so trains can and are running, they just don't want flight passengers to go to the airport.
[1] https://www.nationalrail.co.uk/service-disruptions/heathrow-...