Hello, I need a plugin for Lightroom Classic that allows automatic background transparency and the application of a loaded image to be applied to the background of a series of images in print mode.

I know it doesn't exist yet. That's the principle of evolving according to needs! I'm familiar with using PNG ID plates overlaid on the image, but this is different. Lightroom Classic now allows the creation of masks. It's easy to lighten a background to the point of making it white. It shouldn't take much to make it transparent. Then, of course, we need to make it possible to add a new background, with or without locking, and to position it. If the ability to make transparency is already implemented, the biggest step has been taken.

I doubt you will find anything like that.  Lightroom-Classic does not recognize transparency, neither does it edit with layers. (It does allow layered PSD TIF files in the catalog)

You will need a pixel editor app like Photoshop.

In the Lightroom-Classic print module the closest you will come is to create a PNG image (with transparency) in the same ratio as your camera files, then use this as an Identity Plate Overlay. eg a Frame: