Support has been added to the Execute SQL dialog and Update SQL dialogs that allows users to save and load SQL queries to/from .sql text files. This replicates the functionality available in the DB Manager over to the core browser-based database connection facilities.
The UX has been designed to mimic the same functionality from other standard parts of QGIS, such as the Processing Script Editor with Toolbar actions for Save/Load as well as new actions for other standard operations, including copy, paste, undo, and redo.