Problem 1 - Storage Space
Presumably you have replaced the 64GB iPad Air2 (pictured right) with the much newer iPad10 (pictured left) that may similarly also have only 64GB of internal storage...
The newer iPad10 will undoubtedly be running iPadOS 18.x - of which the iPadOS Operating System software will itself occupy significantly more of the 64GB total internal storage than will be the case for your older iPad Air2 running iPadOS 15.x.
As such, the new iPad will have less available "free" space for user-data and files. If you have almost filled the available storage of your iPad Air2, this will likely explain the issue with insufficient space being available to transfer existing data from the iPad Air2 to the new iPad10.
Assuming that my assumptions and conclusion are correct, regrettably, you are always going to struggle with an iPad that has so little internal storage. The 32/64GB devices are primarily intended for use in Educational settings, or in environments where the ability to store local data on the device is not required.
It is generally recommended that you always maintain at least 4-6GB of free storage space at all times - as your iPad needs some temporary space to complete many tasks. When performing system software updates, or initially transferring data between devices, you may temporarily require more...
If your internal storage is full, or is insufficient for the task that you need to perform, your only option is to better manage the storage that you have - and delete unused Apps or unneeded data.
I note from the above screenshots that you have not subscribed to Apple's iCloud+ storage service - and as such are restricted to the free-of-charge 5GB iCloud storage quota. For a very small monthly subscription, this can be increased to 50GB - which may help with managing the limited internal storage available to both your old and new iPads. Other storage plans offering significantly more cloud storage are similarly available:
iCloud+ plans and pricing - Apple Support
Buy iCloud+ or upgrade your current storage plan - Apple Support
These support pages may prove to be helpful:
About storage on your device and in iCloud – Apple Support
What's the difference between device storage and iCloud storage? – Apple Support
Manage your iCloud storage – Apple Support
How to check the storage on your iPhone, iPad and iPod touch – Apple Support
Clear Other storage on your iPhone or iPad - Apple Support
“Offloading” Apps can be a helpful method of creating temporary space - in particular for a software update:
https://9to5mac.com/2020/01/21/how-to-offload-apps-in-ios-to-save-space-without-deleting-their-data/
Additional information about creating sufficient space for installation of a software update can be found here:
If you need more space for an update on your iPhone, iPad, or iPod touch - Apple Support
External storage options can often help with managing limited internal storage. Depending upon your iPad model, the iPad will either have a Lightning or USB-C port - and may therefore require either an Adapter or USB hub to connect the USB Storage device. If your iPad has a Lightning port, you’ll need an Apple Lightning to USB3 Camera Adapter:
- Lightning to USB 3 Camera Adapter
https://store.apple.com/xc/product/MK0W2ZM/A
Problem 2 - AppleID
When setting-up the new iPad, you should not be attempting to create a new AppleID - as, presumably, you intend to use the existing AppleID account as already being used with the old iPad Air2. When setting-up the new iPad, pay attention to the set-up prompts.