If you need to list the post categories on every page, then yes, sharing them is necessary. The warning is only against unnecessary sharing of data, since you can always pass page-specific props from the controller.
If they're only used on a subset of all pages, you can create a separate middleware where you share them with Inertia::share(). You can then apply it to only the necessary route groups.
Either way, post categories doesn't sound like a lot of data, so sharing them will not impact performance in any meaningful way.
If there were tons of categories and fetching them were an expensive DB operation, you could combine lazy loading and caching on the backend, together with partial reloads on the front end. But it's not necessary here. You might still want to cache them for a few seconds, though, if your site has a lot of traffic and they're fetched from the DB.