I feel we have been down this route before?
Quite.
HSR appeared in 2017, with a proposal not very different to Airtrack.
I don't think there ever was a thread on this forum about the original Airtrack proposal and its consultation and TWA application and public enquiry (2008-2011). In 2011 the Government declared they would not fund it at all, and BAA first "deferred" their application and then
the next year dropped it altogether. They gave as reasons the objections raised to the effect on some level crossings, and difficulty finding all the money themselves.
The technical issues, such as what kind of electricity was possible where, were all worked out at that stage, as was the route and issues such as the SSSI on Staines Moor. The most difficult bit to build was the recreation of the western chord which bypasses Staines East Junction - across what is now the car park of Elmsleigh Shopping Centre, and requiring the demolition of the access bridge over the A308. When
WRAtH▸ came along that created a conflict for access to T5 from the west, but what the status of that is now in unclear - if Airtrack can rise from the dead ...
I still think (as I did at the time) that it would be easier, and make more sense, to start with just the line from T5 to a new bay at Staines Station, and extend Heathrow trains (presumably Crossrail) to it. That provides connectivity, even with the need to change trains and (to go west) platforms. If the demand is there, linking to the lines eastwards is relatively easy. I suspect the chord would never be justified except as a bribe by BAA, though of course if Heathrow expansion ever becomes a real project BAA will need some of those.