OK: I found the old source and I'll try to outline it (trust me it's a bit one-off since it's not usued in the production so it's easier to explain in english).
The most important bit is the public transit API: it allows returning travel times between addresses or geographic coordinates. For stockholm there is the trafiklab api which is excellent, and free. https://www.trafiklab.se/api/
A naive implementation would just generate the map by taking each map pixel, figuring out the lat/lon on the map, and calling the transit API to get the color of the pixel. That however will be painfully slow (a year?) since the API will throttle/limit the number of calls.
So a better approach is to sample some subset of points and interpolate. Most of the larger city area is not populated so a lot of time would be wasted trying to query transport times from places in water or forrests. The best solution I could come up with was to use a list of addresses, because those say where people live. So I needed a list of addresses either with lat/lon coordinates, or a service that could give me lat/lon from the addresses (Such as openstreetmap). I found a real estate api at Booli that provided a large number of addresses including lat/lon. Perfect. I just made a simple script to dump a large list of many thousand addresses to a little db I had.
So I loop all the addresses in my address list, using a timer to throttle the transit API calls to the allowed rate. The results (coordinate, transit time) I insert into a QuadTree for perf - a list would work just as well but finding the nearest point later would be slow as hell.
After that is done, I generate map tiles. For each pixel of each tile I get the lat/lon, and then do a lookup in the QuadTree for the closest known point within some max_walking_distance (I chose 2km) for which I know public transit (Taking the shortest travel time if there are several). This can now run completely offline so will complete generating maps for all the zoom levels in not many minutes (I chose zoom levels 5..14 which covers the use case nicely).
The app itself is then just a static html with some google maps api calls to serve the overlay map from the static tile images.
Thanks