Polygons inside polygons QGIS

You can use Vector general > Join Attributes by Location tool in Processing Toolbox(Ctrl+Alt+T).

1. Set Input layer to municipality layer
2. Set Join layer to hydrological regions layer
3. Select within only
4. Select only ID field in Multiple selection window
5. Set Join type to Take attributes of the first matching feature only (one-to-one) and run the tool

You can use the tool join attributes by location : https://docs.qgis.org/3.10/en/docs/user_manual/processing_algs/qgis/vectorgeneral.html#join-attributes-by-location

He is located in the tab Vector -> Data Management Tool

It allows you to choose 2 layers and the spatial relation to join attribute from one layer to the other (intersect, touches, within, etc...). You can also choose the column to join.

In the pictue layer_A will be your municipalities, layer_B your Hydrological Regions and the Geometric predicate is within. So every municipalities obtain the ID of the Hydrological Regions they are in.