We investigate the coexistence of task-oriented and data-oriented communications in a IoT system that shares a group of channels, and study the scheduling problem to jointly optimize the weighted age of incorrect information (AoII) and throughput, which are the performance metrics of the two types of communications, respectively. This problem is formulated as a Markov decision problem, which is difficult to solve due to the large discrete action space and the time-varying action constraints induced by the stochastic availability of channels. By exploiting the intrinsic properties of this problem, we first simplify it and convert it to an equivalent Markov game, for which the large and discrete action space issue is greatly relieved. Then, we propose a Whittle’s index guided multi-agent proximal policy optimization (WI-MAPPO) algorithm to solve the considered game, where the embedded Whittle’s index module further shrinks the action space, and the proposed offline training algorithm extends the training kernel of the conventional MAPPO to address the issue of time-varying constraints.