If you want to batch style your layers you may select the source layer, right click on it and choose
Then select your target layers keeping the
Ctrl key pressed.
Eventually, go to the
Layer menu and choose
I've noticed that the
Paste style menu is activated only when the target layers are similar to the source layer.
You can easily paste your copied style in a text editor, using
Ctrl+V to study it.
Or you can save the initial layer style in the
.sld file format, in a separate folder called
QGIS styles, for example.
Then, when you create a new layer, just browse the
QGIS styles folder for a convenient style. This way, styling will become an integrated part in the new layer creating process.
A better approach, especially in a medium with more developers involved, you can save/load your
layers' styles directly in/from the database: