I don't have a recommendation, just some random thoughts about the options presented.
Any way you go about it, if you're doing it because you're expecting excessive settlement of the slab relative to the wall foundation, the solution is likely to be less than ideal. Minimizing the settlement would seem a prudent step regardless of the configuration chosen.
If you extend the slab through the doorway and let it float, how do you not end up with a gap under the door? The door frame is on the foundation, and if the slab sinks, there will be a gap under the door. However, if you extend the foundation across the doorway, and stop the slab at the inside face, you have the potential for lip at the doorway. It would seem the choice between those 2 options would depend on what's under the door. Is there a raised threshold at the door frame, or just a sweep on the bottom of the door? If you have a raised threshold, then there's lip at the door already, so any small change due to settlement is inconsequential - it's already a bit of a step up to the doorway. If it's just flat through the doorway (or sloped to the outside for drainage, which would be advisable), then you have to accommodate any settlement with an adjustable sweep on the bottom of the door (unless we're talking about an overhead door, in which case there is no issue).
The third option is with the slab supported by the foundation, which doesn't cause any problems for the door, but could cause issues with the slab, if the slab settles. Then you have potential cracking issues, as well as possible issues with any rainwater that makes it way around or under the door running toward the middle of the floor. The cracking could likely be mitigated with thickening and/or reinforcement in the slab, but the potential for puddles in front of the doorway could be a trickier issue. Providing a positive slope greater than the potential settlement could be an option, but possibly difficult to execute. Careful detailing to minimize potential for water to get in through the doorway may work, but I've never seen that approach be successful in the long term.