How to load sqlite extension in PDO?

No way present now except workaround mentioned above. If you would want to check progress somewhere in the future, there's an issue on PHP bugtracker.

I have implemented a library with a solution for this problem for PHP 7.4+ which does not involve recompiling the PDO driver. In short, it uses PHP's FFI extension and Z-Engine (which reads PHP's internal memory structures using FFI) to make a direct call to the SQLite C API. You can find more detailed background information in this blog post. I would not recommend this solution in production yet, but it could be a feasible workaround for test or development workflows.

could not find a compiler flag and we have solved it with a quick'n dirty hack in pdo_sqlite extension. patched sqlite_driver.c with sqlite3_enable_load_extension() from sqlite3 API.

--- php-5.3.7.old/ext/pdo_sqlite/sqlite_driver.c    2012-01-06 11:04:44.000000000 -0500
+++ sqlite_driver.c 2012-01-06 08:16:58.000000000 -0500
@@ -718,6 +718,8 @@
        goto cleanup;
    }
 
+   sqlite3_enable_load_extension(H->db, 1);
+
    if (PG(safe_mode) || (PG(open_basedir) && *PG(open_basedir))) {
        sqlite3_set_authorizer(H->db, authorizer, NULL);
    }