So that's actually a feature called Handoff. It's one of the features that's a part of the Continuity features. Basically, it lets you transfer something you do on one device to another.
If you'd like to turn it off, you can do that without disabling AirDrop depending on what device you're using. To turn it off on macOS, head over to System Preferences>General>Allow Handoff between this Mac and your iCloud devices, and turn that checkmark off.
To disable Handoff on your iOS and iPadOS devices, head over to Settings>General>AirPlay & Handoff, and disable the "Handoff" toggle. If you have an Apple Watch, disabling Handoff on your iPhone should disable it on your Apple Watch as well.
Here's an article if you'd like to learn more about Handoff: https://support.apple.com/en-gb/guide/iphone/iphcec5d0a9d/ios
Have a lovely day!