> Does Bangladesh have a systemic prescription opiate problem?
If you want to talk about the impact of opiates on Bangladeshi poverty today, you should go back much further in history.
Bengal opium, being much higher quality than the product found in China and Afghanistan, was the major impetus behind the British annexing the territory back in 1757. They used this monopoly to extract exorbitant taxes from Bengal, causing widespread man-made famines which killed tens of millions of people. They then used this tax money and the opium to flood the Chinese market with cheap, high-quality opium, against the Chinese rulers' will, in an attempt to undermine the Chinese government as well by creating a widespread opiate epidemic. China did not come under explicit colonial rule the way Bengal did, but it came very close.
Over this time period, Bengal went from being the richest region in the second-richest empire/region in the world (next to China) to one of the poorest, which it still is today, despite its rapid growth in recent years.
This strategy isn't over, by the way. The opiate market was (and still is) a part of the US military strategy in Afghanistan - balancing the desire to "crack down" on heroin production and smuggling against the desire to provide Afghani civilians with an agricultural economy that doesn't rely on Taliban support.
Bangladesh doesn't have a synthetic opiate problem, simply because people there are generally too poor to purchase synthetic opiates in the first place. Raw opium is still used in these areas due to its widespread availability, but it's much less addictive than the synthetic opiates, because pharmaceutical synthetics are obviously designed to be highly concentrated and potent.
As for the raw numbers, 0.3% of Bangladeshis consume opiates at least once per year, compared to 0.57% in the US, 0.8% in Italy, 2.65% in Afghanistan (the highest) and 0.004% in Singapore (the lowest).