Apple has not removed this feature.
Copy and paste between Apple devices is part of Universal Clipboard, which is included in Apple's Continuity features and is still supported in current versions of macOS and iOS.
If the feature stopped working after an iOS / macOS update, the most likely explanation is that one of the required Continuity settings changed or the connection between the devices needs to be refreshed.
The first thing to check is that Handoff is enabled on both devices.
On the Mac, open System Settings, select General, then AirDrop & Handoff, and make sure that "Allow Handoff between this Mac and your iCloud devices" is turned on.
On the iPhone, open Settings, select General, then AirPlay & Continuity, and confirm that Handoff is enabled.
Both devices should be signed in to the same Apple Account with two-factor authentication enabled. Bluetooth and Wi-Fi should also be turned on, and the devices should be near each other because Universal Clipboard relies on these services to communicate.
If there is a Commercial VPN installed, whether it is being used or turned off . Remove the VPN as per the developers instructions
If all of these settings are correct, restarting both devices often restores the connection after a software update. It is also worth checking that both devices are running the latest available software updates.
If the problem continues, turning Handoff off on both devices, restarting them, and then turning Handoff back on has resolved the issue for some users.
If that does not help, signing out of the Apple Account on the affected device and then signing back in may refresh the Continuity services.
Apple provides detailed information about these features in the following support articles:
Universal Clipboard:
Use Universal Clipboard to copy and paste between your Apple devices - Apple Support
Handoff:
Hand off tasks between Apple devices - Apple Support
Continuity:
Use Continuity to work across Apple devices - Apple Support
Apple Intelligence may have been used for the wording; the technical content reflects my own experience