What is the right way to mark the far right lane as an exit only lane?

Looking at this section:

https://www.openstreetmap.org/edit#map=19/37.78859/-121.98134

(680 Southbound, just north of Crow Canyon Rd exit)

The far right lane becomes an exit only lane at this spot. I looked into the motorway_junction and also using the :lanes tag but neither were clear to me if they were correct or even possible.

Background: I believe Tesla uses OSM and for this particular spot, Tesla Navigate on Autopilot puts you into this lane even though you are not taking this exit. So right at the very end when the lane has actually started merging, Tesla tells you to get out of the lane, which is impossible at this stage of driving.

Did you look at the turn-key: https://wiki.openstreetmap.org/wiki/Key:turn ?
The bottom part of the picture “Motorway with links and destinations” has more or less what you need.
Just do not add “through” for the far right lane (“B” in the example).

Nice, I didn’t find that. So looking at that, it seems I can edit it this way:

none|none|none|none|right

Since there are 5 lanes and the far right lane is an exit only lane. Only other question is what is the best way to make this edit? Should I edit each node of the road (the selectable dot on openstreetmap.com) until the turn?

you should split the OSM way where the right lane starts showing the that it is an exit lane. This can be with markings on the pavement or with signs next to the road. The other split is at the point where the exit physically starts separating from the highway.
Put the tags on the way segment you created.

You do not have to add additional tags on the nodes.