Check generation and tool
In old worlds, already created chunks and new chunks may differ. Don't apply the old Y=11 rule to modern generation with negative heights. The Y coordinate in Java is visible on F3, in Bedrock it is enabled by setting the display of coordinates. Reference: Java ore distribution 1.18.
Diamond ore is mined with an iron pickaxe or better. A stone one will destroy a block without a diamond. For the first descent, take two picks, a bucket of water, torches and non-flammable blocks.
Dig a tunnel network you can navigate
Go down the stairs, saving the exit coordinates. Make the main passage the height of 2 block, then the side branches of the same height. Leave 2 solid blocks between parallel passages - this is a simple plan for inspecting the walls, not a mathematical maximum of loot.
Light the same side and place a sign at each return to the highway. Deep slate is mined more slowly than stone; don't expect the same number of blocks per minute at different heights.
The instructions cover the descent, lava and navigation in the tunnels: Safe mining: descending, branching and working near lava.
Expose the vein before mining it
Lava underground is more dangerous than the height itself. Stand on a solid floor, open the sides of the vein and seal the holes at the bottom, then mine. Do not dig vertically underneath you.
Without enchantment, diamond ore usually yields one diamond; Fortune increases production, Silk Touch saves the block itself. If the first find is for a pickaxe, mine 3 diamond with an iron tool, and additional veins can be marked before obtaining Fortune.
If you want a different mining result, compare the two pickaxes: Fortune or Silk Touch: which pickaxe should you make first?.
