extract project/backend aspects of api-exec-await

[haraldschilly]

Description

This is just the project, backend and types aspect of #7722

The new code should be backwards compatible, but it's saner to do this in 2 phases and make sure there is either the old code (before the recent async changes) or the new code being used.

Checklist:

• Testing instructions are provided, if not obvious
• Release instructions are provided, if not obvious

[williamstein]

I hit this test failure once on my laptop:

│ FAIL ./reuse-in-flight.test.ts (10.337 s)
│   ● reuseInFlight › different args
│     expect(received).toStrictEqual(expected) // deep equality
│     - Expected  - 1
│     + Received  + 1
│     @@ -4,8 +4,8 @@
│         0,
│         0,
│         0,
│         1,
│         1,
│     -   2,
│     +   1,
│         1,
│       ]
│       61 |     ]);
│       62 |
│     > 63 |     expect(res).toStrictEqual([0, 0, 0, 0, 0, 1, 1, 2, 1]);
│          |                 ^
│       64 |   });
│       65 |
│       66 |   test("ignoreSingleUndefined", async () => {
│       at Object.<anonymous> (reuse-in-flight.test.ts:63:17)

It worked when I tried again.