iPad Pro (3rd gen) stuck in recovery mode after charging

Sorry, I forgot, that you can only check the Battery Health on an iPad Pro M4, the newest 2025 model.

But, you could contact the official Apple Support and ask them to diagnose your iPad Pro online.

Depending on the age and use, the battery might have to be replaced by Apple.

iPad Repair and Service - Apple Support

But, also check which apps used the iPad battery most just before the iPad shut down.

And, have a look at the "Insights and Suggestions" part.

Your iPad being in recovery mode suggests that the iPad suffered an unexpected OS-corruption. This type of event is rare, but can occur for a variety of reasons.

Having successfully restored the iPad, in this case your iPad is a recent model that supports restoration using an iPhone, the iPad will have been fully reset including erasure of its internal log files. As such, any evidence of what might have caused the issue is not available - and you are unlikely to be able to determine what caused the problem.

With the iPad successfully restored, unless the problem reoccurs, you have no reason to be concerned. If the problem does repeat, you would be well advised to seek assistance directly from Apple Support and request a remote diagnostic of your iPad. You can contact the Support Team using the Support link at top-right or bottom-left of this page.

Alternatively, you might visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to test and assess your iPad. If a fault is identified, you'll be in the best possible place to explore your available options:

Genius Bar Reservation and Apple Sup

Did you already check the Battery Health in the settings?