Correction, I just double checked the order and it's actually as follows: (Source: https://www.irs.gov/irm/part21/irm_21-006-003r)
21.6.3.4.1 (10-03-2022) Nonrefundable Credits Procedures Nonrefundable credits are applied in the order that they appear in this section, unless stated otherwise in the specific credit section, form instructions, or publication: Form 1116, Foreign Tax Credit (Individual, Estate or Trust) Form 2441, Child and Dependent Care Expenses Form 8863, Education Credits (American Opportunity and Lifetime Learning Credits) Form 8880, Credit for Qualified Retirement Savings Contributions Form 5695, Residential Energy Credits *Credit for Other Dependents *Child Tax Credit Form 3468, Investment Credit Form 5884, Work Opportunity Credit Form 6478, Biofuel Producer Credit Form 6765, Credit for Increasing Research Activities Form 8586, Low-Income Housing Credit Form 8830, Enhanced Oil Recovery Credit Form 8826, Disabled Access Credit Form 8835, Renewable Electricity, Refined Coal, and Indian Coal Production Credit Form 8844, Empowerment Zone Employment Credit Form 8845, Indian Employment Credit Form 8846, Credit for Employer Social Security and Medicare Taxes Paid on Certain Employee Tips Form 8820, Orphan Drug Credit Form 8874, New Markets Credit Form 8881, Credit for Small Employer Pension Plan Startup Costs and Auto-Enrollment Form 8882, Credit for Employer-Provided Childcare Facilities and Services Form 8900, Qualified Railroad Track Maintenance Credit Form 8864, Biodiesel and Renewable Diesel Fuels Credit Form 8896, Low Sulfur Diesel Fuel Production Credit Form 8904, Credit for Oil and Gas Production from Marginal Wells Form 8906, Distilled Spirits Credit Form 8907, Nonconventional Source Fuel Credit (carryforward only) Form 8908, Energy Efficient Home Credit Form 8910, Alternative Motor Vehicle Credit Form 8911, Alternative Fuel Vehicle Refueling Property Credit Form 8923, Mine Rescue Team Training Credit Form 8932, Credit for Employer Differential Wage Payments Form 8933, Carbon Oxide Sequestration Credit Form 8936, Qualified Plug-in Electric Drive Motor Vehicle Credit Form 8834, Qualified Electric Vehicle Credit Form 8941, Credit for Small Employer Health Insurance Premiums Form 5884-A, Employee Retention Credit for Employers Affected by Qualified Disasters Form 8994, Employer Credit for Paid Family and Medical Leave Form 8881, Credit for Auto-Enrollment Form 8801, Credit for Prior Year Minimum Tax - Individuals, Estates, and Trusts Form 8839, Qualified Adoption Expenses Schedule R, Credit for the Elderly or the Disabled Form 8910, Alternative Motor Vehicle Credit Form 8936, Qualified Plug-In Electric Motor Vehicle Credit Form 8396, Mortgage Interest Credit Form 8859, Carryforward of the District of Columbia First-Time Homebuyer Credit Form 8834, Qualified Electric Vehicle Credit Form 8912, Credit to Holders of Tax Credit Bonds
So the Residential Energy Credit is one of the few that DOES get applied before the Child Tax Credit. (But Adoption Expenses is still after. RIP)