You can run 'find usages' on the annotation. This counts for all lombok features; for example, if you use 'find usages' on a @Data or @Value annotation, it'll find constructor calls (we had to choose one of the many things that are generated as the one that is found for this sort of operation; the constructor seemed like the most logical thing). Same goes for @EqualsAndHashCode (I believe we decided that equals wins that fight), @ToString, etc.
synthetic is a property of methods generated by the compiler to plaster over leaky abstractions between the language model and the bytecode model. synthetic methods and fields are completely ignored by javac; any attempt to call them or refer to them act as if the method doesn't exist. The only way to call a synthetic method is to use reflection, or to handcraft bytecode to do it. We can't use synthetic for this reason.
This @category stuff is fascinating. I don't think we can ever meaningfully use this (we'd have to generate javadoc, and categories are for more than just eclipse outline views, so just blithely assigning @category generated everywhere is going to have unintended side effects), but at least if eclipse has this feature we might be able to patch it to think that lombok-generated stuff has a 'lombok' or 'generated' or whatnot category.