The Third Generation Partnership Project (3GPP) recently introduced the fifth-generation (5G) new radio (NR) sidelink to enable vehicle-to-everything (V2X) communications supporting advanced safety services. Nevertheless, improvements over the previous generation still pose challenges to meet the reliability and latency requirements of V2X communications, particularly in the allocation of distributed resources, i.e., Mode 2. In Mode 2, vehicles autonomously select radio resources for their message transmissions and can maintain the selected resources for a given reservation period to efficiently handle periodic data traffic. However, potential collisions during this period may remain undetected due to half-duplex communications and unacknowledged broadcast transmissions, resulting in persistent message losses and posing a threat to road safety. This paper aims to improve the 5G NR-V2X sidelink for systems beyond 5G-Advanced by exploiting full-duplex transceivers. We propose a novel medium access control (MAC) scheme where vehicles can detect collisions while transmitting, dynamically adapt the collision detection threshold according to the measured channel load, and react to detected collisions through appropriate resource reselection and retransmission procedures. Extensive simulations conducted under various settings show that this MAC scheme brings substantial performance gains in terms of reliability and latency, compared to the current legacy Mode 2 procedure and a benchmark full-duplex scheme from the literature.