This is not a Content Translation issue.

The TemplateData JSON blob in the template in the target language must be defined with the correct "Suggested wikitext formatting" value (in Japanese: 推奨されるウィキテキスト書式). The Japanese template didn't have any value there. I decided to Be Bold and changed it to "block", which is usually appropriate for infoboxes. Subsequently, I was able to publish a draft translation of the same page into my user space, and the infobox wikitext was written with the correct spacing.

A few tips for the future:

1. Suggested formatting should be defined in TemplateData for every infobox. As for everything else with templates, there must be an option to make it global, but for now, make sure you do it every time you import a template from English.
2. TemplateData has some caching issues. If you change the value of "Suggested wikitext formatting", it won't work immediately, but after some time. Perhaps @matmarex or @ssastry know how much time exactly.
3. I recommend that someone who knows Japanese and who is experienced with advanced wikitext editing complete the localization of the TemplateData extension into Japanese. Direct link: https://translatewiki.net/w/i.php?title=Special:Translate&group=ext-templatedata-user&language=ja&filter=&optional=0&action=translate .