Synthetic multivariate time series data with correlation between signals

For testing some classifiers, I want to generate a synthetic time-series data with 3 signals, and a single label which should depend on all data points in all three of them, these are the rules I want my signals to follow:

1. The three signals should have some correlation between them
2. The label should depend on all points on all three signals
3. It should not be linearly separable, and it should be a hard problem for classifiers to handle. (Specifically, I do not want a simple bidirectional LSTM model to achieve an accuracy of above 80%)

I tried many ways which I am including one of them here to give a sense of what I am trying to do:

Generate a base sinus signal over time with a random frequency (in my example I used values between 7 8 9 10 for frequency) and a random phase, the problem is to find this frequency so label (y) depends on frequency (if frequency bigger than 8 y is 1 else y is 0) then I generate 3 random filters and convolve this base signal 3 times to generate my 3 signals I add noise in each step.

freq = np.random.choice([7, 8, 9, 10])
phase = np.random.rand() * 10
base = []
for i in range(data_size):
   base.append(np.random.rand() + math.sin(phase + float(i/freq)))
for f in filters:
   signal = np.convolve(base, f)
   signal += np.random.rand(len(signal)) * 6
   all_features.append(signal)
if freq > 8:
   y = 0
else:
   y = 1

The problem with this data is that a simple BiLSTM model achieves an accuracy of around 100% on it. So my question is that is there any way to achieve this? Do you know any library which I can use to generate this?

If you can provide an example in any programming language it will do, for example, I found simstudy package in R which I think can be used here, however, I do not know how to achieve this in there.

Thank you for your help.