As you already know, the Apple Wireless Keyboard (Model A1016) was introduced in the early 2000s and uses an early Bluetooth implementation. While this keyboard was originally compatible with many Macs and some earlier Apple mobile devices, it is not officially supported with modern iPad models, including the 10th-generation iPad running current versions of iPadOS.
Although the keyboard may appear in Bluetooth device searches in some situations, successful pairing depends on support for older Bluetooth profiles, security methods, and authentication standards. Modern versions of iPadOS are designed to work with newer Bluetooth keyboards and may not support the legacy pairing protocols used by the A1016 keyboard.
As far as I know, because of these hardware and software compatibility limitations, there is no supported method to guarantee that an A1016 keyboard can be paired with a 10th-generation iPad. Standard troubleshooting steps such as restarting the iPad, resetting Bluetooth settings, replacing the keyboard batteries, and removing other paired devices are unlikely to resolve the issue if the incompatibility is due to the keyboard's age and Bluetooth implementation.