Can someone explain this line of Typescript Code?

Let's break this down.

(user.customClaims || {role: ""}) is an expression that result in a value (let's call it 𝒳).

If user.customClaims is a true value, then 𝒳 is user.customClaims. Otherwise 𝒳 is {role: ""}

as { role?: string } tells TypeScript that 𝒳 is a value which conforms to the type { role?: string }.

It does not alter the value of 𝒳 at all.

If 𝒳 has extra properties then it keeps them, but TypeScript doesn't know about them.

Consider:

const foo = { role: "a", value: { x: "y" } };
const bar = (foo || {role: ""}) as { role?: string };
console.log(bar);

bar has a value property so the output of this will be:

{ role: 'a', value: { x: 'y' } }

but if you change the last line to console.log(bar.value); TypeScript will error with:

Property 'value' does not exist on type '{ role?: string | undefined; }'.

If 𝒳 hasn't got a role property then it still doesn't. Since the type definition makes the role optional, then that isn't a problem.

If 𝒳 has a role property but it isn't a string, TypeScript will believe the value is a string so you could get a runtime error.

Consider:

const foo = { role: { x: "y" } } as unknown;
const bar = (foo || {role: ""}) as { role?: string };
console.log(bar.role?.charAt(0));

This will error at runtime because objects, unlike strings, don't have a charAt method.

(NB: In this simple example, TypeScript knows enough about the object assigned to foo that it can work out as { role?: string } is a mistake if I don't use as unknown first).