The LeftSideBar in my project is quite the same. I am facing a similar issue here. When user (try to) log out, they are not actually logging out.

here are the code snippets that might be helpful -

const { signOut } = useClerk();

const handleLogout = async () => {
        await signOut();
        router.push('/sign-in'); // Redirect to sign-in page after logout
    };

            <SignedIn>
                    <div className="flex cursor-pointer" onClick={handleLogout}>
                        <Image
                            src="/assets/logout.svg"
                            alt="logout"
                            width={24}
                            height={24}
                        />

                        <p className="text-light-2 max-lg:hidden px-4" >
                            Logout
                        </p>
                    </div>
            </SignedIn>

Have you resolved the issue? Tell me about it.