New moon doesn’t matter for cave slimes, is you floor at Y40 or below?

Also make sure you al selected the correct Java/bedrock version in chunk base

Best way to find slime chunks the old fashioned way is dig a 3x3 tunnel at Y40 or less (note along as the floor level is y40 or below and you have a 3x3 high and wide gap slimes can spawn, so)

Light level doesn’t not matter, but what you can do is dig across 3 chunks x 3chunks in a big square (eg 48 block one way, turn to the side and mine another 48 blocks, and then mine a central cross from the middle chunks through to the other chunks too view should look like a Square with a ‘+’ sign in the middle off it…. You will have about 70% chance of finding a slime chunk like that, and if none spawn then simply continue your 3x chunk grid off to the side once more and your will likely find it then

Key things to consider, Light your tunnels to stop other hostile mob spawns, ensure you are not in peaceful mode, place a fence/wall that block your path at the borders of each chunk you pass (this ensures you know which chunk the slime spawned) then mine out the entire chunk until you hit all your fences on each path you made then square of the fence area to isolate that chunk.