Pretty much in any world, I make a point to find and develop a village. Farmers are the prime emerald source early on - carrots/potatoes to get them out of novice, then pumpkins. Once you have an axe with silk touch, melons are even better. Once iron farm goes up, toolsmiths/weaponsmiths/armorers are unlimited xp and emeralds. And infinite supply of diamond armor and tools. Even without the zombifying and curing, librarians and cartographers are a massive source of free xp. Buy glass from former, make panes, sell to the latter. If either are both are zombied/cured, it is also an infinite emerald generator.
By trapping a villager in a boat in an enclosed space one can rapidly cycle through their first level trade by placing the workstation/checking villager/breaking workstation until you get the trade you want. One can have librarians with all the good trades (Mending, Fortune 3, Silk Touch, Unbreaking 3, Protection 4, Efficiency 5, Infinity etc) real fast as long as you do the prep work of putting up enough beds and optimizing their farms so you get a lot of villagers quick.
The only diamonds I ever need to actually mine/find are those for an enchantment table.