BUG: `Styler.to_excel` does not export styles and formats correctly
This is a tracker / explainer for the various issues:

- (#21221)
- (#25185)
- (#30008)
- (#34438)

Essentially these issues record 3 things:

### Set_table_styles

`Styler.set_table_styles` is **not** exported to excel. This will not be changed (at least by me). To write xlsx, excel styling needs to be attached on a per-cell basis, whereas in HTML indirect references can be created in the CSS language that the browser will parse, for example `thead th` will apply to all header cells in the header section, and `tbody th:nth-child(3n+0)` will apply to every third header cell in the body section starting with first. Without writing our own HTML to cell translator for the CSS language it is therefore impossible to map and account for all the complex CSS rules that can be used within `set_table_styles`. **This is well documented**.

Todo:

 - [x] We will instead propose changes that allow styling to header cells, to complement that already in place for body cells, (#41995)

### Exporting formatting

The number of possible formatting constructs allowed by Python is greater than what excel offers. Excel also has specified structures that differ from Pythons structures. It is impossible to dynamically code these relationships in some ambiguous cases. Therefore this will not be implemented.

Todo:

- [ ] There is currently a pseudo CSS attribute: `number-format` which can be used to apply specific Excel based formatting. This should be much better documented with examples.

### Border styles bug

Borders in CSS can be specified in many different ways, and the parsing code to translate this into excel's border structure is broken

Todo

- [ ] Review the border CSS translation code and propose a solution, if only to document a single way of getting this to work.
