bpo-44958: Revert GH-27844 (GH-28574)

This reverts commit 050d1035957379d70e8601e6f5636637716a264b, but keeps
the tests.
diff --git a/Modules/_sqlite/cursor.c b/Modules/_sqlite/cursor.c
index 9bac607..38ccdcf 100644
--- a/Modules/_sqlite/cursor.c
+++ b/Modules/_sqlite/cursor.c
@@ -104,7 +104,12 @@
     Py_CLEAR(self->row_cast_map);
     Py_CLEAR(self->lastrowid);
     Py_CLEAR(self->row_factory);
-    Py_CLEAR(self->statement);
+    if (self->statement) {
+        /* Reset the statement if the user has not closed the cursor */
+        pysqlite_statement_reset(self->statement);
+        Py_CLEAR(self->statement);
+    }
+
     return 0;
 }
 
@@ -116,14 +121,6 @@
     if (self->in_weakreflist != NULL) {
         PyObject_ClearWeakRefs((PyObject*)self);
     }
-    if (self->statement) {
-        /* A SELECT query will lock the affected database table(s), so we need
-         * to reset the statement to unlock the database before disappearing */
-        sqlite3_stmt *stmt = self->statement->st;
-        if (sqlite3_stmt_readonly(stmt)) {
-            pysqlite_statement_reset(self->statement);
-        }
-    }
     tp->tp_clear((PyObject *)self);
     tp->tp_free(self);
     Py_DECREF(tp);
@@ -518,19 +515,18 @@
         }
     }
 
+    if (self->statement != NULL) {
+        /* There is an active statement */
+        pysqlite_statement_reset(self->statement);
+    }
+
     /* reset description and rowcount */
     Py_INCREF(Py_None);
     Py_SETREF(self->description, Py_None);
     self->rowcount = 0L;
 
     if (self->statement) {
-        /* A SELECT query will lock the affected database table(s), so we need
-         * to reset the statement to unlock the database before switching
-         * statements */
-        sqlite3_stmt *stmt = self->statement->st;
-        if (sqlite3_stmt_readonly(stmt)) {
-            pysqlite_statement_reset(self->statement);
-        }
+        (void)pysqlite_statement_reset(self->statement);
     }
 
     PyObject *stmt = get_statement_from_cache(self, operation);
@@ -553,6 +549,8 @@
             goto error;
         }
     }
+
+    pysqlite_statement_reset(self->statement);
     pysqlite_statement_mark_dirty(self->statement);
 
     /* We start a transaction implicitly before a DML statement.
@@ -572,7 +570,6 @@
             break;
         }
 
-        pysqlite_statement_reset(self->statement);
         pysqlite_statement_mark_dirty(self->statement);
 
         pysqlite_statement_bind_parameters(state, self->statement, parameters);
@@ -590,6 +587,7 @@
                     PyErr_Clear();
                 }
             }
+            (void)pysqlite_statement_reset(self->statement);
             _pysqlite_seterror(state, self->connection->db);
             goto error;
         }
@@ -648,9 +646,13 @@
         }
 
         if (rc == SQLITE_DONE && !multiple) {
+            pysqlite_statement_reset(self->statement);
             Py_CLEAR(self->statement);
         }
 
+        if (multiple) {
+            pysqlite_statement_reset(self->statement);
+        }
         Py_XDECREF(parameters);
     }
 
@@ -802,6 +804,7 @@
     sqlite3_stmt *stmt = self->statement->st;
     assert(stmt != NULL);
     if (sqlite3_data_count(stmt) == 0) {
+        (void)pysqlite_statement_reset(self->statement);
         Py_CLEAR(self->statement);
         return NULL;
     }
@@ -812,7 +815,7 @@
     }
     int rc = pysqlite_step(stmt);
     if (rc == SQLITE_DONE) {
-        Py_CLEAR(self->statement);
+        (void)pysqlite_statement_reset(self->statement);
     }
     else if (rc != SQLITE_ROW) {
         (void)_pysqlite_seterror(self->connection->state,
@@ -982,7 +985,11 @@
         return NULL;
     }
 
-    Py_CLEAR(self->statement);
+    if (self->statement) {
+        (void)pysqlite_statement_reset(self->statement);
+        Py_CLEAR(self->statement);
+    }
+
     self->closed = 1;
 
     Py_RETURN_NONE;
diff --git a/Modules/_sqlite/statement.c b/Modules/_sqlite/statement.c
index 3016fe5..b20c91d 100644
--- a/Modules/_sqlite/statement.c
+++ b/Modules/_sqlite/statement.c
@@ -360,31 +360,23 @@
     }
 }
 
-void
-pysqlite_statement_reset(pysqlite_Statement *self)
+int pysqlite_statement_reset(pysqlite_Statement* self)
 {
-    sqlite3_stmt *stmt = self->st;
-    if (stmt == NULL || self->in_use == 0) {
-        return;
-    }
-
-#if SQLITE_VERSION_NUMBER >= 3020000
-    /* Check if the statement has been run (that is, sqlite3_step() has been
-     * called at least once). Third parameter is non-zero in order to reset the
-     * run count. */
-    if (sqlite3_stmt_status(stmt, SQLITE_STMTSTATUS_RUN, 1) == 0) {
-        return;
-    }
-#endif
-
     int rc;
-    Py_BEGIN_ALLOW_THREADS
-    rc = sqlite3_reset(stmt);
-    Py_END_ALLOW_THREADS
 
-    if (rc == SQLITE_OK) {
-        self->in_use = 0;
+    rc = SQLITE_OK;
+
+    if (self->in_use && self->st) {
+        Py_BEGIN_ALLOW_THREADS
+        rc = sqlite3_reset(self->st);
+        Py_END_ALLOW_THREADS
+
+        if (rc == SQLITE_OK) {
+            self->in_use = 0;
+        }
     }
+
+    return rc;
 }
 
 void pysqlite_statement_mark_dirty(pysqlite_Statement* self)
diff --git a/Modules/_sqlite/statement.h b/Modules/_sqlite/statement.h
index cce81ed..b901c43 100644
--- a/Modules/_sqlite/statement.h
+++ b/Modules/_sqlite/statement.h
@@ -44,7 +44,7 @@
                                         pysqlite_Statement *self,
                                         PyObject *parameters);
 
-void pysqlite_statement_reset(pysqlite_Statement *self);
+int pysqlite_statement_reset(pysqlite_Statement* self);
 void pysqlite_statement_mark_dirty(pysqlite_Statement* self);
 
 int pysqlite_statement_setup_types(PyObject *module);