Rare but probably not as rare as you might think, given that the game (Java Edition) makes 50 attempts per chunk at placing emerald ore (for comparison, prior to 1.18 there were only 3-8 attempts per chunk, making it 9 times rarer, and on Bedrock if it had the same generation), and on Bedrock Edition it actually does generate in veins of up to 3 with 100 attempts per chunk (up to 300 total), making it an ordinary find (these differences are always so odd given the drive towards feature parity):
Emerald ore attempts to generate 50 times per chunk in blobs of 1, from levels -16 to 320, being most common at level 256, and becoming less common toward either end of the range. Emerald ore can be exposed to the sky, which is intended.[1] In Bedrock Edition, emerald ore attempts to generate 100 times per chunk in all types of windswept hills or mountains biomes in blobs of 0-3 ores, from levels -16 to 320, being most common at level 256, and becoming less common toward either end of the range.
So I was messing around in Creative mode in a 1.18.2 vanilla world with commands, until I saw a 3 VEIN of EMERALDS!!!
HOW RARE IS THIS?
Besides this I realized there were still 15 OTHER EMERALDS IN THIS CHUNK!
Bonus: I Found a Mineshaft in a Amethyst Geode!
Rare but probably not as rare as you might think, given that the game (Java Edition) makes 50 attempts per chunk at placing emerald ore (for comparison, prior to 1.18 there were only 3-8 attempts per chunk, making it 9 times rarer, and on Bedrock if it had the same generation), and on Bedrock Edition it actually does generate in veins of up to 3 with 100 attempts per chunk (up to 300 total), making it an ordinary find (these differences are always so odd given the drive towards feature parity):
TheMasterCaver's First World - possibly the most caved-out world in Minecraft history - includes world download.
TheMasterCaver's World - my own version of Minecraft largely based on my views of how the game should have evolved since 1.6.4.
Why do I still play in 1.6.4?
Because you need to have a 'reason' to play both and have them feel distinct, given they will never feel the same.
emerald is still hard to find even in bedrock
if mojang really wanted feature parity i think they would have done it instead of trying to create 3 mobs each year for mob votes