After adding a Query element in the page editor, the only way to add query template or pagination elements is through the small “Quick add” menu. I believe it should also be possible to add those elements through “Block inserter” menu.
You can see the detailed description of a problem in this video:
- WordPress version: 6.0
- Gutenberg Plugin version: -
- Cwicly Plugin version: 220.127.116.11
- Cwicly Theme version: 1.0.3