However, I'm having trouble finding a definitive source for the recommended transmission speed for Cat 3, Cat, Cat 5e, Cat6, and Cat6a twisted pair cables. In fact, some of these sources seem to contradict each other.
This is not at all surprising. The cable categories are determined by a number of standards bodies around the world. While they are often the same, or similar enough to be so, they do not always agree on their definitions.
In the United States, this is TIA and (was) EIA (then ECA, now ECIA). On a more international scale, you have ITU, ISO and IEC. Enough alphabet soup yet?
An example of the differences is that ISO/IEC have defined cable categories 7, 7A, 8.1 and 8.2, none of which are currently defined by TIA.
Does anyone know where the various Category cables speeds are defined for Ethernet?
The IEEE Ethernet standard (802.3) does not define cable categories. This is not something for which the IEEE has been given authority to create standards as there are other standards bodies that are responsible for those standards.
Instead, it defines characteristics of the cable that are necessary for the operation of 802.3 traffic.
Or is it the case that Cable categories are not defined a speed?
Six of one, half a dozen of the other.
Seriously, when speaking strictly or technically, no the cable categories do not define speed. They define the maximum frequency (i.e. Hertz) of the signal that can be reliably communicated on the cable and a number of characteristics the cable must have to meet that need and be certified.
On the other hand, the maximum frequency the cable can sustain reliably does impact what speeds of data communication can/should occur on that cable. However the maintainers of the cable category standards do not define speeds for the cables because different methods may result in different speeds (Ethernet versus serial, etc).
Well that's fine, until you open several book on [insert certification] preparation that clearly states xxx...
So yes, when it comes to details like this, it can be confusing and you can find conflicting information. However when you are dealing with certifications, you will be best served checking official certification prep materials and simply accepting that you will need to memorize some information in a way that is required for that particular certification provider.
Whether you use slightly different information in the real world or never use it at all (looking at you Classful networking), the point is you will need to know it for the certification.