I was thinking of the three legal states as:

• not logged in (null or {isAdmin: false, isLoggedIn: false})
• logged in as non-admin (false or {isAdmin: false, isLoggedIn: true})
• logged in as admin (true or {isAdmin: true, isLoggedIn: true})

which leaves {isAdmin: true, isLoggedIn: false} as an invalid, nonsensical state. (How would you know the user’s an admin if they’re not logged in?) Of course, in a different context, all four states could potentially be distinctly meaningful.

My preferred way of modelling this would probably be something like
role: "admin" | "regular" | "logged-out"
or
type Role = "admin" | "regular";
role: Role | null
depending on whether being logged out is a state on the same level as being a logged-in (non-)admin. In a language like Rust,
enum Role {Admin, Regular}
instead of just using strings.

I wouldn’t consider performance here unless it clearly mattered, certainly not enough to use
role: number,
which is just about the least type-safe solution possible. Perhaps
role: typeof ADMIN | typeof REGULAR | typeof LOGGED_OUT
with appropriately defined constants might be okay, though.

Disclaimer: neither a professional programmer nor someone who regularly writes TypeScript as of now.

a === b returns true if a and b have the same type and are considered equal, and false otherwise. If a is null and b is a boolean, it will simply return false.

I would certainly rather see this than {isAdmin: bool; isLoggedIn: bool}. With boolean | null, at least illegal states are unrepresentable… even if the legal states are represented in an… interesting way.