Whistleblower Protection Improvement Act of 2021 This bill establishes, modifies, and expands certain whistleblower protections for federal employees, including with respect to petitions to Congress, whistleblower identity, and protected disclosures. For example, the bill prohibits personnel action against employees who exercise their right to petition or furnish information to Congress and specifically precludes the President, Members of Congress, members of the uniformed services, and other federal employees from interfering with this right. It also generally prohibits employees from disclosing the identity of whistleblowers to individuals outside of the government and allows the Inspector General to determine whether to investigate a referral if the referral is found to have been made in retaliation for whistleblowing activity. Employees may request corrective action from the Merit Systems Protection Board with respect to such prohibited practices and may file an action in court if the board does not render a final decision within 180 days of a request. The bill also expands the list of recipients to whom an employee may make a protected disclosure to include a supervisor in the employee's direct chain of command. It also includes personnel actions involving furloughs of more than 14 days but less than 30 days, and furloughs of 13 days or less that are not due to funding lapses, as appealable adverse actions that are subject to certain procedural requirements.