SegWit who want to extend the functionality of Bitcoin, and as part of this extension, they want to split the transaction for storage in two chains (is this correct?) The important section regarding the amount of the transfer and the history link stay in the existing blockchain, but because of the reduction in information, more transactions can be stored in a block.
While this is 'kind of true', it elides some vital detail. The fact of the matter is that any node that wishes to operate in a trustless manner must still validate the signature information. IOW for trustless nodes, there is no data reduction.
This solves the size problem in the short term,
Well, no. Only for non-fully-validating nodes. All nodes that ignore the signature chain will need to trust other -- fully-validating nodes (which get no capacity boost) -- to do the validation for them.