A custom Assistant is the intersection of three things - Model, Internet, and custom prompt instructions (and a few other settings).
Two things about the current UI don't seem quite right
As a user I want to start a Custom Assistant session and change the model mid-stream.
- Because the dropdown includes both CA and Model, if I chose a Model then i lose the fact that I was in a Custom Assistant
- Prior to changing the model, when in a CA, i dont know what the model is
I think the solution might be to have two dropdowns, one for Custom Assistant and one for Model. You already have Web access seperate from Model/CA, this would be an extension of that UI choice.
Then you'd have in the CA field "<default>" to mean that no CA was selected.
If you went a step futher you might change the naming of CA to Profile or Project.
Another benefit of this is right now the CA and Model llist is too long (see other feature request)

More user configurability between CA and Model selections.