docs: seed the SQL reference from DataFusion 54, and cross-link it

The function catalogue is now real rather than a pointer. Scalar functions are
listed by taxonomy -- math, string, unicode, regex, date/time, array, map,
struct, crypto, type -- and the names come from what datafusion-functions 54
actually registers, not from what DataFusion documents on main. Aggregate and
window pages gain the same treatment.

Two things the audit corrected rather than copied.

SHOW TABLES does not work. DataFusion implements it over information_schema,
which this session does not enable, so it fails at plan time. It was documented
as working here, on the SHOW page and in three Manage tables; all four are
fixed, and the SQL overview now lists the absence alongside SHOW COLUMNS.

Prepared statements are a Flight SQL protocol feature, not a PREPARE statement.
A script carrying PREPARE ... AS SELECT will not run, while the same intent
expressed through a client will. The new page says so rather than copying
DataFusion's syntax.

Every section of the Documentation tab that has a SQL counterpart now links to
it -- 27 of 76 non-SQL pages, each pointing at the specific statement rather
than at the reference index.

docs/web/sql/aggregation.mdx

@@ -47,20 +47,54 @@ is before deciding to refresh it again.
 
 ## The function set {#functions}
 
-The aggregates are DataFusion's, and the full list is in its
-[aggregate function reference](https://datafusion.apache.org/user-guide/sql/aggregate_functions.html):
+Registered in DataFusion 54. Names below are what is actually available.
 
-| Kind | Examples |
-| --- | --- |
-| General | `count`, `sum`, `min`, `max`, `avg` |
-| Statistical | `stddev`, `var`, `corr`, `covar`, `regr_*` |
-| Approximate | `approx_distinct`, `approx_percentile_cont`, `approx_median` |
-| Collecting | `array_agg`, `string_agg`, `first_value`, `last_value` |
+**General**
 
-The approximate ones are worth knowing about on a large table:
+```text
+count  sum  min  max  avg  median
+bit_and  bit_or  bit_xor  bool_and  bool_or
+first_value  last_value  nth_value  grouping
+```
+
+**Statistical**
+
+```text
+stddev  stddev_pop  stddev_samp
+var  var_pop  var_samp
+corr  covar_pop  covar_samp
+regr_slope  regr_intercept  regr_count  regr_r2
+regr_avgx  regr_avgy  regr_sxx  regr_syy  regr_sxy
+```
+
+**Approximate**
+
+```text
+approx_distinct  approx_median
+approx_percentile_cont  approx_percentile_cont_with_weight
+percentile_cont
+```
+
+**Collecting**
+
+```text
+array_agg  string_agg
+```
+
+The approximate functions are the ones worth reaching for on a large table.
 `approx_distinct` answers "roughly how many distinct values" for a fraction of
-what `count(DISTINCT ...)` costs, which matters when the column has high
-cardinality.
+what `count(DISTINCT ...)` costs, which matters most where it is most expensive
+— a high-cardinality column.
+
+`DISTINCT` works inside an aggregate: `count(DISTINCT category)`. `FILTER`
+narrows one aggregate without narrowing the others:
+
+```sql
+SELECT
+    count(*) AS total,
+    count(*) FILTER (WHERE score > 0.9) AS confident
+FROM documents
+```
 
 ## Aggregating a sample {#sampling}