For my entire life I thought only the EBU or commonwealth or someone recognized him, and the Eder Jofre bout was for the vacant, unified title? But now it seems boxrec and Wikipedia recognize him as a linear world champ.... Hmnn.... My respects to Johnny as a boxer, regardless!
Alphonse Halimi was recognised as champion by the NYSAC as well as by Britain and Europe when he lost to Caldwell. So Caldwell has a reasonable claim.
To my knowledge Halimi was both NBA and lineal champion when he lost to Beccera, who subseqently retired. Caldwell was recognised as champion by the EBU, whilst Jofre won the vacant NBA title by beating Sanchez in 60. Jofre is generally considered lineal from beating Caldwell in 62, if not before. Whilst there are, of course, alternative interpretations, I find this site best represents conventional consensus on the lineage of each division throughout history - https://boxing.fandom.com/wiki/List_of_lineal_boxing_world_champions
my grandfather coached Caldwell for a couple of months or so while Caldwell was based in Glasgow, it might have been longer. and No, I don't remember anything mentioned about Caldwell specifically, though it was during the same few years that my grandfather was Coaching & Training top Scottish Fighters namely, Walter McGowan, Cowboy McCormack, Chic Calderwood and lesser known fighters like Charlie Parvin among others. A real strong period for Scotland from the 1930s to the 1970s.
I do not follow BW or FW but the IBU/EBU and Commonwealth were major titles and at times their champion was considered the lineal or "real" one. The fact they usually weren't is how these bodies became regional. This was a bit later then other instances but it was before they formed the WBC and that shift formally happened. In the pre alphabet era whenever there were 2 claimants who fought there has been a modern tendancy to give it to the guy who won the unifier ex post facto. And to play down the dispute as if the winner had the recognition all along. Caldwells titles becoming regional the year after he lost would only reinforce this.