You need to put in an extra logical test in your OR function that tests for start times less than the time interval start and end times greater than the time interval end. So in cell G31 your formula should read:
=IF(OR(COUNTIFS($A$3:$A$14,A31,$C$3:$C$14,">0",$D$3:$D$14,">=14:00",$D$3:$D$14,"<15:00"),COUNTIFS($A$3:$A$14,A31,C$3:$C$14,">0",$E$3:$E$14,">=14:00",$E$3:$E$14,"<15:00"),COUNTIFS($A$3:$A$14,A31,C$3:$C$14,">0",$D$3:$D$14,"<14:00",$E$3:$E$14,">=15:00")),"Busy","Free")
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…