No, the NUA distribution does not need to occur within 12 months of separation. However, the distribution of NUA must be part of a lump-sump distribution of the 401(k). To qualify as a lump-sum distribution the entire balance in the 401(k) must be distributed within a single calendar year (one taxable year) and there cannot have been any intervening distributions between the last qualifying event (reaching age 59½, separation from service, or your death) and the beginning of the year in which you perform the lump-sum distribution. All of your distributions after the qualifying event must be in a single calendar year, with the 401(k) being completely distributed before the end of that year.
For example, if you separate from service in 2025 after reaching age 59½, you could wait until 2028 to perform the lump-sump distribution (including the NUA distribution) as long as after separation from service you take no distributions in 2025, 2026 or 2027.
See section 402(e)(4): https://www.law.cornell.edu/uscode/text/26/402#e_4
