When you send an MP3 file to another person through email, AirDrop or iMessage, the file is generally transferred in its original format. iOS does not automatically convert an MP3 file into an M4A file simply because it is being shared or received.
Where the received MP3 file is stored depends on the app you use to open or save it.
By default, iOS provides the Files app as a location where you can save and manage MP3 files. However, the Files app is not the only option. You can also open an MP3 file using a compatible third-party audio player or music application, provided that the app supports the format and offers a suitable storage or import facility.
If an MP3 file is being converted to M4A, the conversion is most likely being performed by the application handling or importing the file, rather than by iOS itself. Some music and audio applications may convert imported audio into their preferred format as part of their import or library-management process.
You have not mentioned which application you are using to receive, open or store these MP3 files. That information is important because the behaviour can vary from one application to another.
Regarding Apple Music:
You can add your own MP3 files to your Apple Music library, but this is not the same as directly transferring an MP3 file into the Apple Music app through AirDrop, email or iMessage.
The usual procedure is:
1. Import the MP3 files into the Music app on a Mac or into the Apple Music app on a Windows PC.
2. If you have Sync Library enabled with an eligible Apple Music or iTunes Match subscription, your music library can sync across your supported Apple devices.
3. You can then access the synced music through the Music app on your iPhone.
In short: iOS does not inherently convert MP3 files to M4A during file sharing. Before identifying the cause, please specify which application you are using to receive and store the MP3 files. That will help establish where and why the conversion is taking place.