I do not have permission to sync new iphone to iTunes

You can only transfer messages through iCloud or by restoring a backup that contains them. This is a security feature.

Why can’t your old phone check for updates?

To update over the air from the phone all of these requirements must be met:

• You need at least 6 GB of free storage
• You must be connected to a Wi-Fi network (and not a personal hotspot) unless it is an iPhone 12 or 13 series with an active 5G network connection
• The phone must be charged to at least 50%, and preferably plugged in so it stays above 50% during the update
• The phone must not be in Low Power Mode
• The phone must not be connected through VPN
• The phone cannot be in Airplane mode
• You cannot still have a beta version installed on the phone

Your main problem seems to be lack of storage. Aggravated by the fact that Apple considers your Mac “Obsolete” (out of support) and your OS is out of date with Mavericks. I think it’s also too old to offload stuff to iCloud, but you might check for that. I don’t see an easy solution, other than to clean up your storage. You might try a disk cleanup program like Omnidisk Sweeper to identify how your storage is being used, to help identify stuff that can be removed.

I said Catalina AND LATER. I assumed you meant Mac OS 12.6 Monterey, which is newer than Catalina. What version of of Mac OS do you have?

if it is older than Catalina then you will need the latest version of iTunes. If you are very low on storage it may not be possible to sync with your computer. However, in iTunes Preferences go to Advanced and click Reset Warnings. It’s a stretch, but it might help.

In Catalina and later you don’t use iTunes to sync (actually, it doesn’t exist), you use Finder. See→Use the Finder to sync your iPhone, iPad, or iPod with your computer - Apple Support