It isn't surprising that it's difficult to find info. Modern publishers strongly dislike giving that kind of technical detail, because it's fiddly, difficult, and they consider it offputting for general readers. For information about the manuscript tradition you need to check a critical edition: not a translation, not a Latin edition for general readers, but a critical edition.
(That would be why you don't find this info in places like Wikipedia either, because Wikipedia editors tend to dislike looking at sources that are (a) hardcopy and (b) not in a modern language.)
Anyway, the principal manuscripts range in date from the 9th to the 12th centuries for the Bellum gallicum, 10th to 11th for the Bellum civile. I haven't checked the most recent critical edition of the BG, but have looked in Klotz' edition of both (BG 1957, BC 1950). Here are his summaries of the manuscripts available, and the phylogenetic relationship between them: Bellum gallicum, Bellum civile.
(Edit: just by way of explanation, by convention, in a stemma like this, Roman letters represent manuscripts that survive; Greek letters represent archetypes that can be reconstructed on the basis of the extant manuscripts.)
The manuscript tradition is in itself one of the main pieces of evidence that Caesar 'wrote an original'. Klotz' analysis is prima facie evidence that the manuscript tradition goes back a good bit further than the extant manuscripts, because they show every sign of having a common ancestor. That implies they were written before the 9th century.
Then there's the fact that the manuscripts explicitly attribute the texts to Caesar. Here for example is the first leaf of the text in cod. Paris. 5763, starting
Incipiunt libri Gai Caesaris
belli gallici Iuliani denar-
ratione temporum
Gallia est omnis divisa in partes tres; quarum unam incolunt Belgae. ... (etc.)
Notice the attribution to Caesar in the heading. If someone wanted to go full tinfoil-hat and suggest that the text was forged in the 9th century, then they'd have to imagine a continent-wide conspiracy that lasted several hundred years without anyone at any point giving the game away.
In general we're happy to take that kind of ascription at face value, but understandably there's reason for some degree of wariness when a celebrity is involved. And, for some texts ascribed to Caesar -- the African war, the Spanish war, and the Alexandrian war -- other evidence compellingly shows that Caesar did not write those ones.
With the Gallic war and the Civil war, fortunately, ancient sources give very ample corroboration of the fact that he wrote them, as do earlier mediaeval sources. Here's how the Brill's New Pauly encyclopedia, Supplements I - Volume 5 : The Reception of Classical Literature, describes their testimony:
The works of C. were subjected to heated and very varied reception in antiquity. Authors produced supplements to C.’s Commentarii, imitating the content and style of the B.G. Counting among works of this type are Aulus Hirtius’ contemporaneous eighth book of the B.G. itself, and the other commentarii of the Corpus Caesarianum. Pseudepigrapha also appeared in C.’s name, their authenticity already questioned in antiquity, e.g. the Acta Caesaris, which according to Cicero Mark Antony had plans to alter (Cic. Phil. 2,109), and two speeches entitled Apud milites in Hispania, which Augustus denounced as forgeries (Suet. Iul. 55). ...
The entry goes on to talk about how Cicero praised the Commentarii (Brutus 262), how Asinius Pollio 'sought in his Historiae to correct the self-portrayal of C., who he said had not written truthfully' (Suetonius Julius 56.7), how Pliny criticised Caesar's conduct in Gaul, and how Livy drew on the De bello gallico for the relevant part of his own history. In conjunction with the manuscript evidence, this is more than enough to demonstrate Caesar's authorship.
Wow, thank you for such a detailed answer. I will read it with confidence now. As if Caeser himself is speaking to me! Thanks!