Bluetooth accessories missing on transferred iPad

I don’t know if the Bluetooth devices on your previous device are transferred to the new device using Quick Start (Use Quick Start to transfer data to a new iPhone or iPad - Apple Support). I would expect them to be transferred if you configure the new device from a backup of the previous device, though.

Alternatively, you could add the Bluetooth devices manually in Settings > Bluetooth by triggering the pairing mode on the Bluetooth device (Connect iPad to Bluetooth accessories - Apple Support).

the first time one connects a bluetooth device to a new device transferred or otherwise

one is required to put the bluetooth device into pairing / discovery mode

how you go about doing so differ from bluetooth device to bluetooth device

The documentation of the device or the website of the manufacturer should describe how

or you can find guides by googling "<insert bluetooth device name> pairing mode" here you need to replace the <> with the name of the device you wish to attempt to pair

I doubt if you can transfer connections to Bluetooth accessories.

When you pair two Bluetooth devices, you're telling them to trust each other. This presumably includes exchange of unique identifiers for each Bluetooth radio.

If you told a new iPhone to trust the same list of Bluetooth devices that the old one did, the new iPhone might trust the devices - but they wouldn't trust it. Why would they? They would have no idea that the unique identifier of the phone was different now. Until reset, they would trust the old phone – which isn't around to pair with them any more.

My guess is that you will need to re-pair the devices you want to use.