Congress Leads by Example Act of 2022 This bill authorizes the Office of Congressional Workplace Rights (OCWR) to investigate alleged violations of occupational safety and health protections in legislative branch entities. The bill also provides certain employment-related protections to employees of such entities. The OCWR shall have subpoena authority to inspect and investigate occupational safety and health complaints in congressional offices and committees, the Congressional Budget Office, the Capitol Police, and other specified entities. The bill also imposes record-keeping requirements on such entities with respect to the enforcement of occupational safety and health protections. Additionally, these entities may not (1) retaliate against an employee for requesting OCWR action or for participating in an OCWR investigation, (2) fire an employee because the employee's wages have been garnished due to a debt, (3) retaliate against an employee for whistleblowing activities, (4) discriminate against an employee for being a debtor or bankrupt, or (5) retaliate against an employee for attending jury service. Other matters addressed in the bill include: authorizing the OCWR to seek, in appropriate cases when an unfair labor practice complaint is filed, court-ordered temporary relief from the practice, such as a temporary restraining order; excluding additional types of proceedings (e.g., proceedings involving discrimination claims) from confidentiality provisions that currently apply; and requiring employing offices in the legislative branch to enter mediation if requested by a claimant (currently, both parties must agree to enter mediation).