Tongue pulls back slightly from the D position, blending into R. Sounds close to 'jr'.

Americans pronounce drugs as DRUHGZ (/drʌgz/). In "drugs", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. This is called the DR Sounds Like JR, a small move that separates 'classroom' from 'native'. It comes out as DRUHGZ. You'll hear it in sentences like "The k-9 unit was brought in to search for drugs".
Record yourself saying "drugs" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 5 sounds. Explore each sound's mouth shape and how it's made.
Tongue pulls back slightly from the D position, blending into R. Sounds close to 'jr'.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Raise the back of your tongue to touch the soft palate. Add vocal cord vibration, then release.

Same position as S, but add vocal cord vibration. Feel the buzz.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "drugs", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. /d/ shifts toward /dʒ/ ("j"), so DR sounds like "jr".