Particle accelerators, among the largest, most complex devices, demand increasingly sophisticated computational tools for the design and optimization of the next generation of accelerators that will meet the challenges of increasing energy, intensity, accuracy, compactness, complexity and efficiency. It is key that contemporary software take advantage of the latest advances in computer hardware and scientific software engineering practices, delivering speed, reproducibility and feature composability for the aforementioned challenges. We will describe the Exascale software stack that is being developed at the heart of the Beam pLasma Accelerator Simulation Toolkit (BLAST). As a highlight, we present how the US DOE Exascale Computing Project (ECP) application WarpX uses the power of GPUs at scale, which won the 2022 ACM Gordon Bell Prize. We will present performance results on the first Exascale supercomputer for the modeling of laser-plasma acceleration. We then describe how we are leveraging the ECP experience to develop a new generation ecosystem of codes that, combined with machine learning, will enable modeling from the ultrafast to the ultraprecise for future accelerator design and operations.