You could get the cpap battery but then how do you charge it when not plugged in? Generator would do it but that is a long run time.
I recommend a small 300w inverter connected to just the circuits you need to run the tv and cpap. Some cpap run direct off 12v so you possibly could just pull some 12v wire.
Small inverter I recommend
GoPower 300w $172 and
15a transfer switch $49For solar charging...
PWM system:
2x 120w $307 panels 20a controller $80This would allow you to skip the dedicated cpap battery.