Strictly speaking, anything other than walking, light stretching, resting, lifting heavy weights, and eating is cutting into your strength and muscle gains. Those attributes are built with specific stimulus and recovery. Cardio is not part of that specific stimulus or recovery and therefore is an interloper. But that's only the case if your single goal is pure strength and muscle, which is a fairly narrow goal.
Greg Nuckols asserts that cardio won’t hugely impact your gains in the short run, and may be beneficial for strength and size in the long run
1) You can still get bigger and stronger with doing strength training
and cardio simultaneously.
2) In the short term, concurrent training (cardio and lifting
together) is about 31% less effective for hypertrophy, and about 18%
less effective for strength.
3) Frequency and duration of aerobic training affected strength and
hypertrophy gains – more frequency and volume of aerobic training
meant smaller strength and size improvements.
4) When looking at the data more closely, mode of exercise mattered.
Running, but not cycling, negatively impacted strength and size gain
However, he also notes that the evidence suggests that low intensity cardio should be prioritized over interval training for the most part.
Being on a caloric deficit already puts strength and muscle gains on the chopping block. Adding cardio might work for your situation or it might nix the little strength gains you're getting while on a deficit. High-intensity interval training is also not specifically what Nuckols is discussing in these studies, and may both interfere more with your strength/hypertrophy training and not give you the benefits he discusses. Furthermore, it's not clear whether a class really qualifies as HIIT, since HIIT generally doesn't take class-sized portions of time. A half hour of "HIIT" is probably misnamed, since high intensity output requires shorter output duration.