I don't know about React-Native library but you can access the underlying Android API's so here is a pointer using the Android API's
But some background first, normally in NFC there is a reading device and a NFC Card. The Reader initialise the NFC comms and the card responds. BUT there is the option of device to device (peer to peer) comms, this uses different underlying comm protocols than device to card
The right hand column of the image below describes it well 
The Peer to Peer method is called Android Beam and unfortunately been depreciated in favour of Bluetooth/Wifi Direct and is not available in Android 10 and above.
Documentation for Android Beam is https://developer.android.com/guide/topics/connectivity/nfc/nfc#p2p
and
https://developer.android.com/reference/android/nfc/NfcAdapter#setNdefPushMessage(android.nfc.NdefMessage,%20android.app.Activity,%20android.app.Activity...)
BUT
there is another more complicated option, it is possible for an Android Device to Emulate a NFC card, this is called Host Card Emulation (HCE), this is probably possible to do on the Raspberry Pi as well.
Therefore one device pretends to be a NFC Card and the other device reads/writes to it as a Card.
With HCE you can emulate a Standard Type 4 Tag and then read/write NDEF messages, the answer here https://stackoverflow.com/a/60813707/2373819 goes in to more detail about how to do this.