Each country sets its own rules for their airspace, so they can do whatever they want. But most have historically deferred to the FAA, but then also Boeing and airlines, and all the regulatory bodies work with ICAO to try and be on the same page as much as possible.
There may in fact be some obscure treaties and trade deals, among ICAO complexities, that complicate sovereignty on this issue.
I think one of the long term implications of this message is that the European aviation authorities will defer less to the FAA and another bit of US 'soft' power is eroded.
They did until the 737MAX had two crashes within a month. This changed everything: the FAA refused to ground this plane until literally every other ATC organization in the world stood up and restricted it from their airspace. The FAA only capitulated to save face after the plane was effectively banned from leaving US airspace.
There may in fact be some obscure treaties and trade deals, among ICAO complexities, that complicate sovereignty on this issue.