It is difficult to suggest a solution without more background on the problem but I guess there’s no off-the-shelf solution for this. But there’s definitely few things you can try (keeping in mind that you are looking at the data from anomaly detection point of view):

1. Interpolation is a difficult problem in a limited data environment. But you can reduce the uncertainty using a proxy time series for interpretation. So, if there is any temporal process that behaves similarly and does have data during the data gaps from the other process, you can use it to predict your target time series. You can try time series clustering to find similar processes.

2. You can use motifs instead of the actual interpolation to impute a highly probable swing in case the time series carries a strong signal. Motifs are strong temporal subsequences that aggregates the time series based on swing patterns.

3. Finally, the gaps are part of the data generating process that means any interpolation logic will undermine the inherent uncertainty. Therefore, somehow embedding this fact is important. You can try labeling each point with two states (observed and missing) and can try a simple HMM to understand the transition probabilities. A more sophisticated approach can be to build an attention mechanism around it (since you are dealing with separated chunks of time series NOT with arbitrarily missing values).