Can I use the Apple Thunderbolt 4 Pro Cable to connect my iPad A2229 to a Studio Display monitor?

Read the related article at the top of this page. From the article:

Use this cable to connect your Mac or iPad to a display that uses Thunderbolt 3 (USB-C) or USB-C for video, such as the Apple Studio Display, Apple Pro Display XDR, LG UltraFine 5K Display, or 23.7-inch LG UltraFine 4K Display. It supports DisplayPort High Bit Rate 3 (HBR3) video output.

MacTracker says that an A2229 is an iPad Pro 12.9-inch (4th generation) (WiFi).

iPad Pro 12.9-inch (4th generation) - Technical Specifications

Apple's specifications say that this model has USB-C, but do not mention Thunderbolt. I think this means that this iPad Pro does not support Thunderbolt.

Studio Display - Technical Specifications - Apple

On the other hand, the specifications for the display say:

"Studio Display is compatible with the following iPad models running iPadOS 15.4 or later [2]:

• iPad Pro 12.9-inch (3rd generation or later)
• iPad Pro 11-inch
• iPad Air (5th generation)"

Apparently it is OK for an iPad Pro or Air with a USB-C port (and a suitable version of iPadOS) to use the display, even though a Mac has to have Thunderbolt to use the display. See:

Set up and use Apple Studio Display - Apple Support