In general, dynamic compression reduces the dynamic range (AKS dynamic contrast) by making the loud parts quieter and/or the quiet parts louder.
That does make everything trend toward the same loudness. It's most-often used with make-up gain to make "everything louder".
If you're shooting for a certain perceived loudness, you may need to make some adjustments after compression.
"Limiting" is a kind of fast-compression. "Automatic Volume Control" or "Leveling" is a kind of slow-compression.
"Loudness matching" is different. It doesn't make any adjustments in the middle of the song/performance. It makes ONE adjustment to the whole track so the dynamic contrast of the original is not reduced... The loud parts of the song remain (relatively) loud and the quiet parts remain (relatively) quiet. ...That may be why it's" not working" for you.
The LUFS feature will get the wave forms close,
LUFS tries to measure the
perceived loudness. Loudness perception is complicated and looking at the "waveforms" is not very good for that.