I’m publishing a book written with v1.99 and starting a new one, hopefully in v3,
Yes, they can run on the same machine at the same time, but the V1 license will not work with V3. When you buy V3 (or get it free if you qualify), you will get a V3 license. See the upgrade information here and here (upgrade guide), the user manual here.
Also, be aware that the project format is different between the two versions. Scrivener 3 can back-convert to the old format, but it’s not automatic.
Great! Thank you both so much!