hp photosmart c4380 driver

Your printer model, 11 years old, does not have a driver by HP compatible with Big Sur. Evidently HP has considered it obsolete like Apple does with Macs that are 11 years old.

Unfortunately the open-source, free Gutenprint print driver does not support your model. 

Try VueScan for scanning. Your printer is supported by VueScan.

If you're looking for a replacement any of the models in this Apple document will be compatible wirelessly via AirPrint with any Mac: About AirPrint - Apple Support

To find out please visit the HP web site. That is where they will be, if they have been released.