In the dawn of the 6G era, edge computing environments have to cope with the increasing demands of nextgeneration cloud-native applications, such as time-sensitive applications. In this context, the application-graph placement problem is further exacerbated by the need to efficiently schedule timesensitive traffic in order to meet stringent latency or other Quality of Service (QoS) requirements. This time-sensitive aspect, which is often overlooked, raises the need for a unified placement and scheduling approach. To this end, we propose a holistic approach to the placement and scheduling problem for time-sensitive applications within edge computing facilities. In particular, we employ Constraint Programming (CP) to compute efficient solutions in a single step, avoiding the limitations stemming from the sequential execution of separate placement and scheduling solvers. Our solution is compliant with industrial Time-Sensitive Networking (TSN) standards (i.e., IEEE 802.1 Qbv). A comparative evaluation among a range of CP variants sheds lights into various aspects, such as the gains stemming from the use of search heuristics.