Both continental and analytic philosophy (if these categories are even coherent and helpful) can be understood as branches of the broader western philosophical tradition, in which Kant is a central figure. So Kant exerts influence on both early analytic and early continental (e.g., phenomenology, hermeneutics, critical theory) traditions. While the historiography of the idea of two distinct traditions is contested, it's often traced to competing reactions against the prevailing neo-Kantianism of the early 20th century, with logical positivists like Carnap et al. going one way and phenomenologists like Husserl and Heidegger going another. Frege is retroactively thought of as part of the emerging analytic tradition because the kinds of questions he asked became central to analytic philosophers, even if Frege was also influential on ostensibly continental figures like Husserl. So in general this is really messy in the beginning but a kind of intelligible 'parting of the ways' (to borrow Friedman's phrase) begins to emerge around this period.