ChatGPT, Custom GPTs, and most other LLMs exhibit the same issue. When generating Japanese text, Markdown bold formatting does not work as expected—asterisks are displayed as-is, like this: マークダウンで**「エラー」**が出ます。
It seems that in Japanese, Markdown bold tags do not function properly when placed directly adjacent to punctuation marks or symbols such as brackets. This issue could likely be resolved by tuning the model to insert spaces on both sides of the double asterisks when applying bold formatting.
Alternatively, one approach would be to train the model not to use double asterisks adjacent to symbols. And, switching to a different Markdown engine that handles symbols more robustly in non-Latin scripts could also be a potential solution.
This article from the Japanese tech blog Qiita is helpful.