Converting / measuring bottle threads for creating an adapter to it
It's really unlikely that a bottle is using nonstandard threads; the engineering and tooling cost for doing so would not make sense. Most plastic drink bottles use PCO 1881 or PCO 1810 threads. If not, it should be one of a number of other less widely used standards.
The industry term for drink bottle thread is &quot;neck finish&quot;. Searching on that, or on one of the standard names like PCO 1881, will find you a lot of information. You can then try to find a match for your threads. Note that the breaks 120 degrees apart do not affect the thread design, and may or may not be part of the neck finish standard, so you can ignore them.
There are existing OpenSCAD libraries for some of these, including

threadlib
IoP-satellite

And some related articles on Hackaday about their development and use:

Learn The Secrets Of Matching Bottle Cap Threads To One Another
Generating Nice Threads in OpenSCAD