Hey plant lovers. I am trying to propagate my Rhapidophora Tetrasperma. I put it in potting soil with some perlite and am keeping the soil moist but the leaves are drooping. Is this normal? Or does it mean it needs more water? I always struggle with the comment "keep it moist but not soggy". It's hard to know where the line is!

Until it forms roots the drooping is normal.
There is an old technique that has been around since plants were cultivated (well, maybe not that long) that seems to have fallen out if common usage (I still do it and some older gardeners I know still do it but largely I don't know any younger gardeners that do it).
When you take a cutting, cuttings should be at a minimum of 2 nodes but 3-5 is better. Strip the leaves off the bottom 1-3 nodes and put that whole section in the media. Then cut the next to the top set of leaves in half and leave only the one very top leaf intact.
This gives the plant a strong base of nodes for new roots to form from simultaneously, and takes the stress of a bunch of leaves off the top that it doesn't have to support and keep alive while rooting.
The leaf material left is enough to photosynthesize and grow new roots but not so much it overly stresses the cutting.
Most people nowadays will not do this especially on variegated plants because they can't let go of the instant gratification of having the leaves

In other words, the leaves are losing water faster than the (small?) roots can supply it. Wetter soil won't change that.
I often trim leaves on cuttings, it also helps show me where the new leaves are, when they grow.