When designing my own color picker, I also faced this dilemma about what to do with out of gamut colors. There were several options, like reducing transparency like you did, or choose some of the methods suggested by Bjorn (oklab author) himself.
But in the end I ended up choosing to neither allow picking it nor even display it because I wanted to also guide/train the user (here myself only for now) about what colors are even present at any given brightness (within srgb gamut). This is important in some extreme cases like very bright colors, where only very few colors are possible to be picked.
Here is one example, I am selecting a very bright yellow-green. There is practically only one hue possible at this level of brightness :
This helps me during painting because if I realize that I need some other hue at this brightness then its something not possible and I need to change something else. If I follow any other out of gamut strategy then the values in the painting will likely be wrong and I will end up realizing it too late. I prefer to get the values in painting as correct as possible, as early as possible.