Any education that takes a deep dive into a subject can be considered specialized training that not everyone receives. For example, musicians might take specialized lessons as teens or earn one or more college degrees later, becoming an expert. Without basic education, advanced education is unlikely to exist, though we can decide by subject; focus on skills characters need. Someone can become an expert without this education, but there are typically gaps in their understanding or knowledge.
If schooling ends before the teens, this type education is unlikely except for nobility and rare individuals. In fantasy settings, we typically see less formal schooling. This suggests special education is rare and therefore private, via an apprenticeship or guild. With its advanced technology, SF suggests that specialized education is widespread, but it depends on the setting. A dystopia may feature a destroyed or depleted infrastructure. Many tools are so easy to use that people need only training in how to design and repair them; we don’t need to work out the education system to determine this.
So what do we need to decide? Mostly how common different kinds of educated learning is, per subject, if they matter to our story. We can make anything rare by limiting the number of resources available to teach it, whether instructors, actual schools, or textbooks. For anything common, colleges or technical schools will teach it. If we need details, determine prerequisites, training duration, subjects taught, the awarded degree, and professions. Unless it’s art, like music, few people get an advanced degree for personal enrichment, but for employment opportunities thus raised. Characters can bond with each other by discussing how much they both hated a subject you decided was disliked.