Unfortunately Bambu’s posture is that of a closed architecture. To use their CEOs words, “walled garden”.
One could explore the MQTT protocol that the printers use but all that would make available is the metadata about printer job status, not what is going on in perhaps the GCode.
There is a thread on resources for the MQTT protocol as it relates to Bambu, with links to open source support for integrating into the Home Assistant protocol, offering many adaptable solutions. If you’re the type of person who got into 3D printing because you enjoy tinkering, this may be right up your alley.