My kid’s approval came in the mail today. The primary difference is that I was granted AF405 (定居) and can immediately convert to HHR, whereas my kid’s was granted AF353 (有直系血親在臺灣地區設有戶籍者) and should need to live in Taiwan.
For those reading this, the optimal step would be to first finish YOUR household registration first before their birth, otherwise the residency requirement will remain for them.