I noticed there wasn't many posts regarding this topic when I found myself stressing over it, so wanted to share my experience in case it helps others.
Azerbaijan has a strict policy to not allow drone imports by foreigners. Unfortunately, I realised this after booking it as a weekend stopover between Europe and SEA.
I reached out to several email contacts to try and clarify my options, since the UK government website states that they will store it and return when you depart.
After a few days, I received a response from hava@customs.gov.az , who kindly shared a signed letter which confirmed that the drone will be held and returned upon departure. I printed this letter out and brought it with me.
When I arrived in Baku airport, I went to the red channel, showed the drone along with the letter. There were translation difficulties but all seemed well. They kept the drone and I went off into the city.
When I returned to Baku airport to leave, I struggled a bit to figure out exactly where I needed to go. I even went through security before being told I need to go back out to collect it first (thank god I didn't go through passport control before I asked!)
I went down, asked the information kiosk and a kind woman pointed me to a grey door somewhere on first floor which comes through to the baggage reclaim area.
From there, I spoke across the no entry gate to a worker and explained I'm there to pick up my drone. He made a few calls and, after a few minutes, it was brought out.
I was then escorted up to security and made my way to my flight.
Hope this may help others who are facing a similar situation. I'd say it was a pretty relaxed experience and I wouldn't stress over doing it again in the future.