my phone spends a lot of time buffering during video play back
See -> About iOS performance on your iPhone, iPad, or iPod touch
About iOS or iPadOS performance on your iPhone, iPad, or iPod touch - Apple Support
Is it possible to pair an iPhone 13 pro max with an external hard drive for photos, videos and music,
Not sure what you mean with 'pair' ?
See -> Connect external storage devices to iPhone
Connect external storage devices to iPhone – Apple Support (UK)
If the iPhone / iPad has an Apple Lightnng connection port, you can use a SanDisk iXpand flash drive to use as an external hard drive. They are available in various sizes.
You can also use that iXpand flash drive as a tool to save the photos to a real external hard drive afterwards.
iXpand Flash Drive are available at Apple Store and at Apple Authorized Service Providers.
iXpand flash drive app can be downloaded from the App Store.
See -> SanDisk iXpand-flashdrive Go
SanDisk 64 GB iXpand Flash Drive Go - Apple
Then download the SanDisk iXpand Drive app from the App Store, see ->
https://apps.apple.com/us/app/sandisk-ixpand-drive/id1079870681