With the arrival of 6G, the Internet of Things (IoT) traffic is becoming more and more complex and diverse. To meet the diverse service requirements of IoT devices, massive machine-type communications (mMTC) becomes a typical scenario, and more recently, grant-free random access (GF-RA) presents a promising direction due to its low signaling overhead. However, existing GF-RA research primarily focuses on improving the accuracy of user detection and data recovery, without considering the heterogeneity of traffic. In this paper, we investigate a non-orthogonal GF-RA scenario where two distinct types of traffic coexist: event-triggered traffic with alarm devices (ADs), and status update traffic with monitor devices (MDs). The goal is to simultaneously achieve high detection success rates for ADs and high information timeliness for MDs. First, we analyze the age-based random access scheme and optimize the access parameters to minimize the average age of information (AoI) of MDs. Then, we design an age-based prior information aided autoencoder (A-PIAAE) to jointly detect active devices, together with learned pilots used in GF-RA to reduce interference between non-orthogonal pilots. In the decoder, an Age-based Learned Iterative Shrinkage Thresholding Algorithm (LISTA-AGE) utilizing the AoI of MDs as the prior information is proposed to enhance active user detection. Theoretical analysis is provided to demonstrate the proposed A-PIAAE has better convergence performance. Experiments demonstrate the advantage of the proposed method in reducing the average AoI of MDs and improving the successful detection rate of ADs.