[ci] Run web tests in wasm (unit + integration). (#8111)
Adds CI configuration to run web integration tests (in the master channel) compiled to Wasm.
It also removes the build-examples step from web integration tests, in some isolated testing:
| platform tests shard | With build-examples | Without build-examples |
|---|-----|-----|
| 1 | 30m | 21m |
| 2 | 13m | 11m |
| 3 | 17m | 10m |
## Issues
* Fixes https://github.com/flutter/flutter/issues/151664