I'm not an Illustrator user, but Inkscape and other programs offer the same feature. According to Adobe's help system, it's called Image Trace in the Illustrator program:
Choose Object > Image Trace > Make to trace with default parameters.
Illustrator converts the image to black and white tracing result by
Results will vary based on the source image, but your image is just about perfect for this feature. The linked page has more detailed information, but I suspect the default settings will give you a suitable result.
In the "Edit the tracing result" portion of the above help link:
When you are satisfied with the results of a tracing, you can convert
the tracing object to paths. This final step allows you to work with
the tracing result as you do other vector artwork. Once you convert
the tracing object, you can no longer adjust the tracing options.
Select the tracing result.
To convert the tracing result to paths, do one of the following:
Click Expand in the Control panel or the Properties panel.
Choose Object > Image Trace > Expand.
The resulting paths are grouped together.
To ungroup the grouped paths, click Ungroup in the Properties panel. Alternatively, choose Object > Ungroup.
(Optional) To simplify paths by removing excess anchor points, choose Object > Path > Simplify. For details, see Simplify a path.
You can also reshape or edit paths. For details, see Adjust path segments.
To color your tracing result, convert it to Live Paint Groups by selecting the desired paths and choosing Object > Live Paint > Make.
For details, see Live Paint groups.