Steroid hormones: how do they travel through the cytoplasm (not just the blood plasma) if they're hydrophobic?
Firstly not all steroid hormones travel inside the cell and regulate the gene expression.
Basically there are two pathways- direct and indirect.
Steroid hormones are lipid-soluble, which allows them to cross the extracellular membrane to the inside of the cell.

Classical models of steroid action suggest that steroid hormones bind to specific nuclear receptor proteins once inside the cell. Reference


Once inside the cell, a steroid hormone binds with receptor proteins in the cytoplasm. The steroid hormone and its receptor form a complex, called a steroid complex, which moves into the nucleus where it influences the expression of genes.
Reference


In the indirect pathway,

The traditional nuclear steroid receptors can also indirectly regulate gene transcription by serving as signal transduction proteins that interact with various signaling pathways in the cytoplasm of a cell. In particular, ER can activate kinases, enzymes that phosphorylate and thereby activate other proteins. This sets in motion a signaling cascade that eventually ends in the nucleus with the induction of gene transcription.
Reference