Currently we exclude all cycleway for our motorvehicles profiles like scooter regardless of the tagging. Scooters can use ferries (see this example) but to reach this particular ferry there is only a cycleway which is currently not possible due to the mentioned limitation although it is tagged moped=yes. But we should be able to fix it for a paid subscription and your custom requirements. Or you can set up your own open source GraphHopper instance and you can implement this.
Less importantly but still useful is… I’d like for scooters to be able to use bike lanes (where allowed).
This is possible (we’ve done similar things for other customers), but it depends on your requirements and also a paid subscription is required (or again, you’d have to set up your own instance).
Furthermore in this particular case it is seems unrelated to bike lanes but instead the oneway restriction leads to the detour. I’m unsure if in your case it makes sense to make oneways a soft constraint (highly unlikely for a motor vehicle), but it is possible too like we do for bikes as one can get off the bike when going the opposite direction of a road.