Would I be eligible for the ISA allowance for the current tax year if I cancel my Cash ISA after the ISA deadline (i.e. in the next tax year) but within OakNorth’s cooling off period?

No. For example, If you open a Cash ISA on 28th March 2022 and cancel the ISA account within the cooling off period of 14 days (i.e. after 5th April 2022 but before 12th April 2022) then you will not be eligible for the £20,000 allowance for the 2021/22 tax year.