Semantic communication (SemCom) with learned encoder-decoder architectures enables end-to-end learning of compact task-oriented representations optimized for the wireless channel, reducing channel resources needed to convey task-relevant information and improving spectrum efficiency. This paper studies semantic image transmission over block Rayleigh fading with AWGN using a multi-task semantic autoencoder that jointly reconstructs images and predicts labels from the received waveform. The latent dimension (complex channel uses per source sample) serves as a cross-layer control variable governing semantic fidelity and channel resource usage. We characterize the resulting latency-task fidelity tradeoff: larger latent representations improve inference accuracy but increase service time, channel uses, and queueing delay. Building on this insight, we develop online semantic-rate controllers that adapt the latent dimension per update under a long-term semantic error constraint. A queue-aware drift-plus-penalty policy minimizes delay subject to an average semantic error cap, while a complementary age-aware policy minimizes time-average Age of Information (AoI). By adapting the semantic rate to congestion and fidelity requirements, the proposed framework improves spectrum utilization and enables timely semantic updates with significantly lower delay and AoI than fixed-rate baselines.