Can an FY21 construction solicitation be awarded in FY22 utilizing FY22 funds without having to resolicit the requirement in FY22?
Yes, as long as the contract includes FAR clause 52.232-18 Availability of Funds whose prescription states "if the contract will be chargeable to funds of the new fiscal year and the contract action will be initiated before the funds are available". You can see the language from that clause copied below protects the Government since funds are not available in your situation. If the contract is going to be incrementally funded, ensure to incorporate DFARS clause 252.232-7007 Limitation of Government’s Obligation.
FAR clause 52.232-18: Funds are not presently available for this contract. The Government’s obligation under this contract is contingent upon the availability of appropriated funds from which payment for contract purposes can be made. No legal liability on the part of the Government for any payment may arise until funds are made available to the Contracting Officer for this contract and until the Contractor receives notice of such availability, to be confirmed in writing by the Contracting Officer.
Air Force Mandatory Procedure 5332.7 Contract Funding has the procedure when issuing solicitations that do not include FAR clause 52.232-18. As such, ensure to understand the applicability of FAR clause 52.232-18.