This paper characterizes the fundamental limits of integrated sensing and communication (ISAC) when the transmitter is subject to an artificial intelligence (AI) representation bottleneck and the receiver employs a fluid antenna system (FAS). Specifically, the message is first encoded into an ideal Gaussian waveform and mapped by an AI encoder into a finite-capacity latent representation that constitutes the physical channel input, while the FAS receiver selects the port experiencing the most favorable channel conditions. We reveal that the AI bottleneck is equivalent to an additive representation noise, which reduces both the communication and sensing signal-to-noise ratios (SNRs) at the selected port. We then derive the resulting ISAC capacitydistortion region and establish tight converse and achievability bounds under general fading models, including Jakes-correlated channels. Leveraging the spatial degrees of freedom (DoF) characterization of the Jakes' model, we furthermore prove that the port-selection gain is fundamentally constrained by the physical length of the FAS region: the effective diversity order equals the numerical rank of the Jakes' correlation matrix and increases only with the FAS length. Consequently, enlarging the FAS length allows the selected-port SNR to approach the AI-imposed ceiling, driving the achievable communication rate and sensing mean square error (MSE) toward their AI-limited fundamental bounds. Numerical results corroborate the analysis and scaling laws.