I think you've stated most of the types of contexts in the question. I would think of them as consisting of three big categories of context for interpretation, and one for application.
The Bible is a collection of individual texts, and so the first category of context is to consider that text as a self-contained piece of literature. What has the author said before this part of the text, and what do they go on to say afterwards? How does this small part of the text contribute to the message of the whole text?
Most of the books of the Bible are long enough to have internal structure too. Sometimes that structure is very clear, other times it's harder to spot. To study a Psalm you should consider not just a verse says in the context of that Psalm, not just what that Psalm says in the whole book of Psalms, but also the place it has within the five 'books' of the Psalms. Each of those five books have distinct characteristics, even though it does sometimes seem like the Psalms have been grouped and ordered arbitrarily.
Some books of the Bible also have a very close connection with each other. Books like 1 & 2 Samuel and 1 & 2 Kings were apparently originally one text which have been divided later on. The twelve Minor Prophets have always been grouped together and so have a closer relationship with each other than they do with Daniel, which in Hebrew Bibles is placed far away from the Book of the Twelve.
In this category we have the historical, cultural, audience, etc contexts. I'm grouping them together here because they're all closely related and intertwined.
Each human author of the Bible was raised in a particular culture at a particular time. They wrote to or for an audience, who may or may not share that culture and time. Many books of the Bible appear to have been edited after their original composition, and so we have potentially another historical context laid over the top of the original.
The later books of the Bible, both the latter parts of the Hebrew Scriptures, and the New Testament, were both written by and for people who had some knowledge of the earlier parts of the Bible. But what they thought about it isn't always clear. Some of the prophets were writing to people who had seen the curses from Deuteronomy be enacted on their nation, but before any relief from God was felt. By the time of the New Testament, we have a complex relationship between the Hebrew Bible and the early Church: their knowledge of the scriptures was largely mediated through a Greek translation, with some substantial semantic differences too. Centuries of theological development had led to more discussion of angels, demons, and the afterlife. And they used religious texts which later Christians have debated and sometimes rejected the inspiration of.
Those who study the Bible who have personal religious convictions usually believe that the scriptures are inspired by God, and so in addition to the human agency that led to their authorship, they are also authored by God. So here we can talk about not just authors who wrote multiple texts (like Solomon or Paul), but how texts from thousands of years apart could have been divinely inspired and purposed. Canonical context will consider how God is progressively revealing himself through the scriptures, through texts which build upon one another, as well as through texts which appear, at least on the surface, to contradict each other. Divinely inspired tensions and juxtapositions in the Bible expose layers of meaning which the human authors may not have been aware of.
Teachers of the Bible also need to consider how the text has been understood and taught over the history leading up to them. This is not hermeneutics proper, but it does inform how we read and teach the scriptures, so we also need to be aware of it. Almost none of us approach the Bible as a clean slate. We come from communities that have read and applied passages in various ways.
Previous generations are our guides - when we come up with a novel interpretation we should consider it carefully, for it is usually more likely that we are mistaken than everyone else in history, especially if you believe that God was guiding them as they read the scriptures. But equally, if our interpretation matches exactly with what you have been given, it's likely you have missed some small nuance in the text; the Bible is just too strange, so there should always be something that makes you question. The person who reads the scriptures and says "Yes I can see what the author is saying here, but there's just one verse that has a weird theological implication" has likely understood the passage better than someone who sees nothing weird in it.
Understanding the context we live in will also help us share the truths of the scriptures more effectively with those around us. There are some heavy topics in the scriptures, and we need pastoral sensitivity to teach them well. For example, no one now can teach Ephesians 5 without being aware of the great harms done by people misreading that passage and using it as a weapon. A sermon doesn't have to explicitly mention how it has been misused before - tangents like that can often be unhelpfully distracting - but the teacher needs to be aware of potential pitfalls so that they can communicate clearly and effectively.