How to approach semi-supervised binary classification problem with few labels only from one class?
I see two approaches:

either you do all your process using only the positive class, so based on one class classification approaches such as isolation forest, one class SVM, recontruction error of autoencoder (trained only by your positive class), and so on... All those classifiers learn from one class.

or you can do it in 2 steps. First try unsupervised approaches (such as clustering) to extract negative (and other positive) class samples. Then use a binary classifier on positive vs negative class. In this approach, you want to be careful with the unsupervised split that give you the input dataset of your second step. You want to avoid mislabeling.