I just did a search of a 21w13a world around the spawn chunks from y=0 to y=255 and got 125 hits on minecraft:emerald_ore.
The lowest is at y=33 and the highest seems to be at about y=110.
However this is in just part of a mountains biome.
Edit: I just expanded my world chunks and searched again.
All 196 hits are at y=33 and above, all in Minecraft:mountains biome.
Depends on the number of attempts per chunk and the amount of terrain within their range; previously the game made 3-8 attempts (average 5.5) per chunk between layers 4-31, with a success rate of around 90% so there were around 5 emerald ore per chunk; I haven't seen anything on the actual density of ores but if this chart accurately depicts the relative concentrations then the majority of emerald is far above sea level, with the peak concentration at y=256, but at that layer it may be more concentrated than redstone used to be (it is definitely not accurate for older versions; it shows the bar for redstone as wide as iron and coal together but coal alone is more common, same for the peak concentration of lapis vs other ores, so I assume the only thing accurate is the relative concentration of each ore over its range).
I surely hope so, at least with diamonds there is an incentive to go mine for them, they're rare, but not so rare that they're boring to strip mine for.
Emerald ore for me on the other hand has been that type of block I generally would mine for only once on a world and unless I have an extra build to decorate with that ore, I'd rather just get the emeralds from trades since it's much easier to get a surplus that way.
I find gold ore to be easier to mine which is weird, considering the advantages gold can give you in terms of armour, tools and potions.
With gold ingots you can make netherite ingots with netherrite scraps, getting you top tier armour and tools, additionally, any worn gold armour plates will cause Piglin to remain neutral.
With emeralds there are additional steps taken to get the stuff you want, so prior to 1.17
the emerald ore mining situation has been disproportionally punishing or unrewarding IMO.