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

Americans pronounce drafts as DRAFTS (/dræfts/). In "drafts", the "t" is squeezed between other consonants and drops out — the surrounding consonants flow together without it — most natural in flowing, casual speech; in careful or formal speech, the T may be lightly present. This is called the Silent T in Clusters, and it's one of the defining features of casual American English. It comes out as DRAFTS. You'll hear it in sentences like "I applied weatherstripping around the door to prevent drafts".
Record yourself saying "drafts" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 6 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.
Drop the jaw noticeably. Keep the body of the tongue low and forward, and don't let the back of the tongue raise toward the soft palate. Pull the lip corners back slightly, almost a starting smile.

Lift your bottom lip to touch the very bottom of your top front teeth. Blow air through this contact point without voicing.

The T is skipped entirely. Your tongue doesn't make contact at the T position.

Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "drafts", the "t" is squeezed between other consonants and drops out — the surrounding consonants flow together without it — most natural in flowing, casual speech; in careful or formal speech, the T may be lightly present. /t/ is dropped entirely — the surrounding consonants flow together without the T.
In "drafts", the "dr" cluster blends into a "jr" sound — a natural American English pronunciation. /d/ shifts toward /dʒ/ ("j"), so DR sounds like "jr".