docs: Incorporate writing table provider blog post to user documentation (#21398)

## Which issue does this PR close?

- Closes #21304.

## Rationale for this change
The existing custom table providers doc was minimal and thanks to
@timsaucer this [blog
post](https://datafusion.apache.org/blog/2026/03/31/writing-table-providers/)
covers the same topic with much more depth. Thus, @alamb opened the
issue for incorporating blog post.

## What changes are included in this PR?
I've replaced content with blog post with some changes: 
- fix several broken URLs (e.g. ParquetSource url was broken)
- made some examples compilable
- fix ExecutionPlan api
- kept table constraints and `using your table provider` sections
- remove acknowledgements and get involved 

## Are these changes tested?
Ran cargo test -p datafusion --doc custom_table_providers — 3 passed, 7
ignored.

Then build with `docs/README.md` instructions and ss for docs:
<img width="1353" height="948" alt="image"
src="https://github.com/user-attachments/assets/7bbac01e-bab2-472e-b5f0-0661ead0249b"
/>
<img width="1358" height="954" alt="image"
src="https://github.com/user-attachments/assets/2f7d1faa-da56-436a-99b1-53afb0073c51"
/>



## Are there any user-facing changes?
documentation only

---------

Co-authored-by: Tim Saucer <timsaucer@gmail.com>

Author: buraksenn