Yeah best not to bombard a 13 with too much information.
It's better to show consistency over a longer period and drop information here and there without referring to trans at all - when opportunities arise remind him that you love him as he is, that boys and girls or men and women can wear what they like, be interested in any kind of hobby, that stereotypes and roles are silly and outdated, point out good role models - like Prince and David Bowie in music were flamboyant but definitely men (assuming he likes music).
Cultivate an interest in science, especially biology. If there's a topical science article about women's or men's bodies, explain the differences. Even in archaeology you can tell the difference between male and female skeletons - you can point that out next time you're in a museum together or something. Talk about biology in other animals - male and female is an evolutionary mechanism and humans are no exception.
Also teach your son about the importance of critical thinking and skills to determine how ideology and beliefs can be used to control people. Use religion and political ideology as a good teaching aide. Like discuss certain cults vs normal faith groups that do not control their followers. How can you tell the difference?
You don't need to venture into debates about trans stuff at all. It's about identifying patterns and signs about 'healthy' ideas and beliefs, and 'unhealthy' ones.
It's about giving your son the skills to help him navigate the world as he grows up. It takes months and years. You're not trying to 'win' arguments and debates with him. Get him to understand that people disagree about all sorts of things all the time, but can still come to mutual respect and understanding by listening to other perspectives.
Discuss court cases like the Christian bakery that refused to write a message about supporting gay marriage, and won. The importance of free speech, freedom to disagree, freedom to not be compelled etc. It will require you to also be informed and learn about these nuanced issues as well.
Who knows, in a few years as he gets older, he might come to realise the arguments supporting trans ideology are fairly illogical and rubbish anyway. 