They use the depot accessibility map. They use the depot accessibility map and follow a predefined route to its stationary destination.
So they choose a direction to go in based on a multitile relevant map of costs and restrictions?
In other words, an algorithm for multitile creature pathing.
Now create a map for every possible creature dimension and keep it updated each time a drawbridge activates or wall is built. Don't forget climbing. It's not a feasible method.
1)
Single Map, not one per creature: each passable tile keeps track of how far away it is from the nearest non-passable tile, that is all.
2) Each creature explicitly stores its narrowest and widest widths and its height for pathing purposes. As well as its squishiness.
3) Totally unsquishy creatures are only allowed to path through parts of the map deisngated as wide enough for their WIDEST dimension (allowing pivoting in any direction with no algorithmic issues or overlap at any time). Totally squishy normal creatures can path through things only wide enough for their NARROWEST dimension. In between can scale in between if relevant.
4) Even if a creature has a path, it still has to check before moving or pivoting whether temporary obstacles like small creatures are occupying that space and react accordingly, not a big deal.
For animation purposes, if a small part of a creature overlaps an unpassable tile, but the map and its squishiness say it's OK anyway, just don't display that tile, and it is abstracted as an extremity squished in around the corner, etc. If not squishy, that wouldn't make sense BUT it won't ever come up if you use widest dimension, so no problemo.
keep it updated each time a drawbridge activates or wall is built.
Very easy for just the one map. You don't even have to check any further than the radius of the largest creature on file from the drawbridge or wall for updating! I.e. a small fraction of one map each time.
Don't forget climbing.
If it proves difficult, then yes, DO just forget climbing. I.e. don't let huge things climb until you feel like getting around to it. Isn't very realistic anyway that a giant sperm whale or whatever could climb without altering the landscape.
Not that I think it would be difficult. It's just a path like before, but pretty much restricted to only EXACTLY the right radius instead of "that radius or higher". Which should ensure that some part is in contact with the wall. Or minor variation of that rule. Worst case, you just simulate the path and project the shape along it ahead of time, still not that bad.