Al-Andalus's empire functions differently than Spain's. They're more interested in trade of manufactured products, cash/staple crops, and slaves rather than pure resource extraction that the Spanish did when they owned New Spain and Peru. Colonization has been pretty light, although it's steadily increasing as Andalusi and Berbers migrate out of the homeland for new opportunities in the Algarves, Africa, and Asia. In fact, they don't even possess the same gold and silver mines that Spain did because it's either not known to them (Cerro de Potosi) or owned by the Otomi Alliance or Iskantisuyu.
They function more closely to mercantile powers like Portugal, Britain, and the Netherlands, which probably won't change as Muslims and Jews will develop concepts like banking and companies due to necessity far earlier than OTL since first contact and colonization had a head start here. In fact, I think Al-Andalus also develops free trade and capitalism far earlier, given exposure to friendly Native/Islamic nations around the colonies instead of hostile Christian powers that England and Spain had, as well as future Sephardic Jew, Golahi Jew, Christian, and Muslim economists being able to discuss ideas with each other in a far more cosmopolitan and urban Europe and West Africa overall. Al-Andalus is also far more stable, as they would focus on a more isolationist stance on European politics, being a Muslim power that doesn't care for Christian religious/dynastic conflicts unless it threatens their interests.
A stable Maghrebi-Andalusian Union in modern MiaJ isn't a 100% possibility though. Nationalism amongst the Berbers could still be a thing and the central government still owns a far more disparate and expansive land than OTL Spain, even if the Andalusi and Berbers are a more closely knit pair of ethnic groups.
Gonig back to economics, slavery will even be far more intensive in this timeline than OTL, once Al-Andalus discovers how extremely productive Mawana, Burinkan, Al-Gattas, and the other Caribbean islands are in producing sugar, as well as cotton, indigo, rice, tobacco, and cannabis production from Meshishib. Al-Andalus has an existing dependence on such cash crops or raw materials for their trade and textile empire, so this will only result in a massive expansion of such cash crop plantations. Even if the Hajib bans chattel slavery, it might inevitably happen due to the control of the cash crop barons or might evolve in a way to exploit loopholes amongst such laws.
In addition, Al-Andalus also has a far higher selection of slaves to choose from, with:
- Siqlabi slaves from Russia, the Haemus, and the Caucasus
- Zanj slaves from the interior of Africa
- Nahua, Quechua and other Native Algarvian slaves as their populations recover from First Contact.
- Heretical Christians from other European polities, making Al-Andalus a dumping ground to keep unorthodox ideas out of their lands.
Sexual slavery would be far more pervasive and open amongst the upper classes, with them having harems or access to both male and female sex slaves/prostitutes, rather than just a slave owner keeping a mistress for their perverted entertainment. It's going to be a far different beast from just standard African chattel slavery, even if slaves might have significantly more political power as soldiers or intellectuals.
Angland is going to set up colonies, most definitely, given their stable political position, high population, and naval expertise. Scandinavian countries like Denmark and Sweden could also find more success than their OTL counterparts in establishing colonies. Lastly, I think the HRE is also an interesting possibility. They are far more centralized than OTL, and the Geroldseck Emperors might see the New World as a land of new opportunity amongst the rise of other Muslim/Christian powers. I doubt France would be able to maintain colonies, given how crippled they are militarily and economically by their separation from Provencia, but it'll be interesting to see them try.
EDIT #1: Reply to Yama951's comment on future Christian colonization of the Algarves.
EDIT #2: Nivek brought up a good point that the Otomi would not be part of the Native Algarvian slaves brought to the Andalusian colonies, but rather the slavers.