It was certainly not a night and day change. The transition to the Neolithic took hundreds, if not over a thousand, years, depending on region and subregion (for instance, the "proto" phase of the Neolithic in the Levant stretches, generally, from 11,700 to 10,500 cal. years BP, a stretch of 700 years). Things happened very gradually, with incremental changes over decades or centuries. In the Near East the PPNA (Pre-Pottery Neolithic A) is found at a scattered (but ever-growing) collection of sites, each of which shared some similarities with the others but also had its own particular flair on this or that element. The most famous of these is probably PPNA Jericho, which was one of the first investigated and also one of the richest as far as quantity and quality of material. In general, the PPNA sites in the Near East show better and different tool shapes than what came before, but there were still plenty of "old" tool shapes around for centuries after the new shapes started to appear. By means of analogy, I can walk around with a smart phone in my pocket in 2021, but I can also go to the thrift store and buy a clock radio from the 1960s that still works perfectly fine.

Another area of glaring difference between "proto"-Neolithic sites and what had come before is architecture. In the southern Levant, differentiation between buildings meant for domestic occupation begin to sharply separate from other, non-dwelling structures in the PPNA. The use of mud-bricks for building superstructures is also new, replacing earlier Natufian use of branches and skins for the same purpose.

And so on and so forth. Imagine slow, incremental changes happening over a fairly large swath of space and time, but also sometimes rapidly, if conditions were right.

For the Near East on this topic, see Simmons, The Neolithic Revolution in the Near East (Arizona 2007). Off the top of my head, there is also a David Miles book about the Neo. Rev. in Britain, The Tale of the Axe: How the Neolithic Revolution Transformed Britain (2016).