process: delay throwing an error using `throwDeprecation`

This makes sure all warnings that were triggered before a deprecation warning during the same tick are properly handled and logged.

It also guarantees that users can not catch the error anymore.

Fixes: #17871 (closed)

Checklist

• make -j4 test (UNIX), or vcbuild test (Windows) passes
• tests and/or benchmarks are included
• documentation is changed or added
• commit message follows commit guidelines