Move some fields (exclude, only, etc) to private API in `Schema.__init__`

Nobody has claimed this yet.

I'd make `exclude` and `only` private API because they are used in `_normalize_nested_options` which is called only at `__init__`.

I'd also make `load_only` and `dump_only` private because setting them after `__init__` conflicts with

```py
self.load_only = set(load_only) or set(self.opts.load_only)
self.dump_only = set(dump_only) or set(self.opts.dump_only)
```

Likewise with `unknown` and `context` due to

```py
self.unknown = unknown or self.opts.unknown
self.context = context or {}
```

(setting them to `None` after `__init__` wouldn't be the same as in `__init__`)

At this point, I'm tempted to make everything private. I mean the attributes above plus `many`, `ordered` and `partial`.

Adding the underscore would break libs using marshmallow (like apispec) but that's life. Or is there another way to signify those are private? Like, just a comment in the docstring?

_Originally posted by @lafrech in https://github.com/marshmallow-code/marshmallow/pull/1258#issuecomment-508262389_

Start by reading Schema.__init__ and _normalize_nested_options, focusing on exclude, only, load_only, dump_only, unknown, context, many, ordered, and partial. Review the compatibility concern for libraries such as apispec before determining whether these attributes should be private or documented as public. Done requires an agreed API direction and corresponding changes, but the issue does not define that decision or name tests.

Written by the indexing model from the issue text.