/db/table/-/count? endpoint, fixed 'count all' button

Closes #2914

docs/changelog.rst

@@ -9,6 +9,7 @@ Changelog
 Unreleased
 ----------
 
+- Fixed incorrect counts when clicking **count all** on filtered table pages. The button now uses a new :ref:`POST count endpoint <TableCountView>`. (:issue:`2914`)
 - Datasette now uses `httpx2 <https://httpx2.pydantic.dev/>`__, the Pydantic-maintained continuation of `httpx <https://www.python-httpx.org/>`__, in place of ``httpx``. The public API is the same, but responses returned by :ref:`internals_datasette_client` are now ``httpx2.Response`` objects rather than ``httpx.Response``. Plugins that use ``isinstance()`` checks against ``httpx.Response`` should be updated to use ``httpx2``. **Plugins that use httpx without explicitly depending on it** will need to add an explicit dependency or switch to `httpx2`.
 
 .. _v1_0_a39:

docs/json_api.rst

@@ -1326,6 +1326,23 @@ The following extras are available for arbitrary SQL query responses and stored,
 
 .. [[[end]]]
 
+.. _TableCountView:
+
+Counting all matching rows
+--------------------------
+
+``POST /<database>/<table>/-/count`` returns an exact count of the rows matching the table's query string filters::
+
+    POST /fixtures/facetable/-/count?state=CA
+
+    {"ok": true, "count": 10}
+
+The endpoint supports the same column, search and plugin filters as the table page. Pagination and display options such as ``_next``, ``_size`` and ``_sort`` do not affect the count.
+
+This requires ``view-table`` permission. ``execute-sql`` permission is only needed if using ``_where`` filters.
+
+Unlike the ``count`` extra, this count is not capped by the row count limit. The usual SQL time limit still applies; a timed-out count returns a 400 JSON error.
+
 .. _TableAutocompleteView:
 
 Table autocomplete