IRS Customer Service and Transformation Act of 2022 This bill requires the Internal Revenue Service (IRS) to submit an initial plan to Congress to address how it intends to meet customer service and technology modernization and related objectives. The IRS must submit semiannual updates to the plan, indicate progress made in implementing the plan, and any changes or challenges in implementing the plan. The bill requires the Government Accountability Office in each calendar year after 2022 and before 2032, to report to specified congressional committees on various matters relating to the IRS, including the progress of the IRS in meeting its objectives and on technology modernization. The bill sets forth customer service objectives that the IRS must accomplish not later than January 1, 2025. It must make available to the public not later than January 1, 2026, certain electronic forms and filing procedures. Finally, the National Taxpayer Advocate is authorized to appoint counsel in the Office of the Taxpayer Advocate to report directly to the National Taxpayer Advocate.