Azerbaijan
Black tea traditionally served in pear-shaped glasses.
Azerbaijan
Kelaghayi silk scarf is worth adding because it feels like something you actually noticed while travelling through Azerbaijan, rather than a generic souvenir. I would avoid the obvious tourist print and look for something with a local pattern, fabric or cut that still works with normal clothes back in the UK. The ideal version is modestly priced, not too bulky, and good enough that you would buy it again even without the holiday memory.
Azerbaijan
This is exactly the sort of thing I like bringing back from Azerbaijan: small enough to fit in a bag, but specific enough to remind you where you bought it. The best version is usually the sealed jar, tin or packet from a normal supermarket, spice stall or food hall, not the most expensive tourist version. It is also the kind of thing you can talk about when someone asks what you brought back, because there is usually a little story attached to where you found it.
Azerbaijan
I would put Azerbaijani black tea on the list for Azerbaijan because it is the kind of thing that feels useful once you are home, not just another airport purchase. It is a good one because people can try it slowly at home, and it makes a nicer gift than a mug with a place name printed on it. The reason it works is that it gives you a quick reminder of the trip without needing to keep a fragile ornament safe forever.