Does the an open source toolchain exist for capturing, processing, and hosting navigable 3D walkthroughs like this (e.g. something like an open-source Matterport)?
Not yet, as far as I'm aware. The current flow involves a DSLR for capture, COLMAP for camera parameter estimation, one codebase for training a teacher model, our codebase for training SMERF, and our web viewer for rendering models.
The big difference is access to fisheye lenses a burst mode that can be run for minutes at a time, and the ability to minimize the amount of camera post processing. In principle, the capture could be done with a smartphone, but the experience of doing so is pretty time consuming right now.
You don't need a toolchain for capturing; you just need the data. Get it now; process it when better tools become available. There are guides for shooting for Photogrammetry and NeRF that are generally applicable to what you need to do.