Use rstcheck to "lint" the README (#17367)

Follow up to https://github.com/element-hq/synapse/pull/17363, so we can
detect issues with the RST file early on.


### Pull Request Checklist

<!-- Please read
https://element-hq.github.io/synapse/latest/development/contributing_guide.html
before submitting your pull request -->

* [x] Pull request is based on the develop branch
* [x] Pull request includes a [changelog
file](https://element-hq.github.io/synapse/latest/development/contributing_guide.html#changelog).
The entry should:
- Be a short description of your change which makes sense to users.
"Fixed a bug that prevented receiving messages from other servers."
instead of "Moved X method from `EventStore` to `EventWorkerStore`.".
  - Use markdown where necessary, mostly for `code blocks`.
  - End with either a period (.) or an exclamation mark (!).
  - Start with a capital letter.
- Feel free to credit yourself, by adding a sentence "Contributed by
@github_username." or "Contributed by [Your Name]." to the end of the
entry.
* [x] [Code
style](https://element-hq.github.io/synapse/latest/code_style.html) is
correct
(run the
[linters](https://element-hq.github.io/synapse/latest/development/contributing_guide.html#run-the-linters))

1 files changed, 1 insertions, 0 deletions

diff --git a/changelog.d/17367.misc b/changelog.d/17367.misc
new file mode 100644
index 0000000000..361731b8ae
--- /dev/null
+++ b/changelog.d/17367.misc
@@ -0,0 +1 @@
+Add CI check for the README.
\ No newline at end of file