How to compare two clustering solutions when their labelling differs
This is only a partial answer since I'm not familiar with HDBSCAN, hopefully somebody else can provide a more complete answer.
As far as I understand you need to find which cluster in A corresponds to which cluster in B, i.e. an alignment between the clusters labels of A and of B. It's not recommended to match based only on the size, since it could happen by chance that a cluster in A has the same size (or similar size) as a cluster in B.
Since the instances are different, you would have to rely on how the method represents the clusters.

For example probabilistic clustering methods represent each cluster as a distribution over the features, so one can use a distance/similarity measure between these distributions.
With k-means one would compare the centroids and match the pairs of clusters for which the distance is the shortest.

I'm not familiar with HDBSCAN so I don't know how the clusters are represented inside the model: whatever this is, the idea would be to compare each internal representation of a cluster in A vs. the same in B.