-ddump-timings -ddump-to-file still outputs to stdout/stderr

Summary

When using -ddump-timings -ddump-to-file I still get quite a lot of output to stdout/stderr:

raider :: /tmp/asdf » ghc -ddump-to-file -ddump-timings asdf.hs
*** initializing unit database:
initializing unit database: alloc=9969256 time=11.402
*** initializing unit database:
initializing unit database: alloc=3184392 time=9.869
*** Chasing dependencies:
Chasing dependencies: alloc=701712 time=0.514
[1 of 1] Compiling Main             ( asdf.hs, asdf.o )
*** Parser [Main]:
*** Renamer/typechecker [Main]:
*** Desugar [Main]:
*** Simplifier [Main]:
*** CoreTidy [Main]:
*** CorePrep [Main]:
*** CodeGen [Main]:
*** systool:as:
Linking asdf ...
*** systool:cc:
systool:cc: alloc=139464 time=0.286
*** systool:cc:
systool:cc: alloc=118560 time=0.248
*** systool:linker:
systool:linker: alloc=1388832 time=1.071

Steps to reproduce

Compile a file with ghc -ddump-to-file -ddump-timings

Expected behavior

Only a .dump-timings file is generated, and the only stdout/stderr output is the standard ghc output, something like this:

[1 of 1] Compiling Main             ( asdf.hs, asdf.o )
Linking asdf ...

Environment

• GHC version used: 9.0 and 9.4

Optional:

• Operating System: Linux
• System Architecture: x86_64