I've got as far as creating a node via the NodeFactory, but where do I set the suffix?
Context's as far as I've seen are read only due to caching.

MetaUtils is deprecated,
API docs don't mention it as far as I've seen

Is it as simple as setting that as a permission on a user?

Check here

I'm talking about doing this programmically, not via commands

Creating a suffix node

Setting the context

Follow the steps outlined here: https://github.com/lucko/LuckPerms/wiki/Developer-API#adding-a-permission-to-a-potentially-offline-user

And then just construct the node using the method @creator3 linked.