Advent Challenge 4: Present Assembly Line!
Charcoal, 96 81 bytes

ＮθＷＳ«→ＦυＧ↗→↙⁺²θ_≔Ｉ⪪ι υ≔⊟υπ≔§υ⁰ρ→↗Ｇ↑⊕π↗⊕θ→⊕ρ↓⊕π↙⊕θ ↑πＰ↗⊕θＰ←⊕ρ↓+↓πＦ²«↷⁴+ρ↷²+π↷¹+θ↶³


Try it online! Link is to verbose version of code. Input is the width on the first line, then the other dimensions on following lines, ending with a blank line. Explanation:

Ｎθ


Input the width.

ＷＳ«


Loop over the remaining lines until the blank line is reached.

→ＦυＧ↗→↙⁺²θ_


Draw the belt between presents. The u variable is predefined to an empty list, which therefore does nothing on the first pass, while later on it ends up with a single element, causing this code to run once. (Using an if would be less golfy.)

≔Ｉ⪪ι υ


Split the dimensions at the space, cast them to integer, and save them in u.

≔⊟υπ


Remove the last dimension and save it in p.

≔§υ⁰ρ


Copy the first dimension to r, but leave it in u so that the belt gets drawn on the next loop.

→↗Ｇ↑⊕π↗⊕θ→⊕ρ↓⊕π↙⊕θ 


Erase the interior of the present, in case the belt overlaps it.

↑πＰ↗⊕θＰ←⊕ρ↓+↓π


Draw the interior lines of the present.

Ｆ²«↷⁴+ρ↷²+π↷¹+θ↶³


Draw halfway around the exterior of the present, then repeat for the other half.