How does Elasticsearch Splitting an Index Work?

It is indeed a problem and it is futher complicated as the delete by query will require a lot of additional disk space, as described in David's response:

I do not think the new shards can get allocated to another node until the delete by query has completed on the original node. Either way it does not work as transferring a 100GB before delete by query runs is not possible.

No. Splitting an index without the required additional disk space will not work.