The Shortbread layer is based on the OSMF-hosted tiles. The tile server is brand-new and there’s no SLA, but it’s designed to have a turnaround time of minutes. If you’re seeing more lag than that, the tile generator might be backlogged or there might be a caching issue.
The MapTiler OMT layer is based on MapTiler’s commercially hosted tiles. They update their tiles “roughly every 2–3 weeks” for their customers, so I’d assume something similar for this tileset.
I made the post a “wiki post” so folks can correct and add to it as needed. We should probably make a more comprehensive guide to these concepts on the actual wiki at some point.