The reason that the air bubble protection needs special attention is that the "triggering event" is considered normal condition, i.e. caused by an empty bag or operator mistake, and with high severity (death). Therefore, if anything to do with the air bubble detector fails (detector, CPU, software), the patient is at significant risk.
The other protection is triggered only if there is a fault in the control system which is rare. If the protection fails, it's not immediately any risk; so a more relaxed timing of the self check is reasonable (e.g. once per day).
I'm not sure about the latest edition, but clearly in the previous edition, the timing for air bubble is separately stated to the other protection systems.
For software: like hardware, if there is separate control and protection, and good design controls (e.g. IEC 62304), the chances of a software bug leading to harm should be very remote because there are two systems.
However, for the air detector, there may be only one software routine. Even with the best design controls, it may not be enough. Good practice would be to have two software engineers write independent routines monitoring the air detector signals. Maybe if the structure of the software simple and well tested, you might be confident. But you need to be 99.9999% sure ...!