For MySQL, you can get the first auto-incrementing integer created from your INSERT from the cursor. If you only inserted one row, congratulations, there’s your PK. If you inserted multiple rows, you could also get the number of rows inserted and add that to get the range, but there’s no guarantee that it wasn’t interleaved with other statements. Anything else you wrote, you should already have, because you wrote it.
For MariaDB, SQLite, and Postgres, you can just use the RETURNING clause and get back the entire row with your INSERT, or specific columns.