are you seriously suggesting the airport for the UK`s second largest city would close ?
There are more long haul services than many imagine. Before covid there was -
3 x daily Emirates to Dubai including the A380
1 x daily Qatar to Doha
1 x daily Air India to Delhi
Pakistan airways frequency fluctuating
2 x daily to Turkish Istanbul
plus many of the European carriers that do not serve such airports as Stansted or Luton
Yes I do believe BHX will suffer, and could ultimately fail. Notice that no US carriers are in the list. So far it has proven impossible for westbound services to make a profit out of BHX. If you want to travel west from the West Midlands you have to either travel into Europe (Air France via Paris, KLM via Amsterdam, and Lufthansa via Frankfurt/Munich), down the M40 to Heathrow (LHR), or up the M6 to Manchester (MAN). HS2 just makes it easier to get to LHR/MAN from Birmingham. The European carriers who you mention also serve Heathrow, generally with a more frequent service.
Emirates/Qatar & Turkish are largely flights to the Far East via Middle Eastern hubs. Post COVID the predictions from the aviation industry bodies (IATA/ICAO) is that hubs will suffer as customers choose direct flights over changing on route.
No chance. Birmingham Airport will be a big winner from HS2.
What will Birmingham Airport gain? New services from East Midlands hub, Chesterfield, Sheffield, Leeds and York. Leeds & York already have direct services into Manchester Airport. I don't see huge amount of traffic suddenly coming from the first three.
Birmingham International is already connected to the WCML, so maybe a bit of time shaved off of Crewe & Wigan, but it will still be as quick to get to Manchester Airport from these places.
In addition it will make it easier to get from the western Birmingham suburbs to get to Heathrow, than now. Many travellers already travel into New Street, to connect to Birmingham International for the airport. Once HS2 is open, the number of flight destinations available via interchanging at OOC will become an hour closer than now.