Based on my experience 20 years ago you could only renew the H-1B visa in the passport in-country under extraordinary circumstances. In the majority of cases they reject your request and would tell you to travel to a consulate.
Prior to the mid 00s you could renew at any consulate but they changed it so you could only renew in your home country.
Prior to the mid 00s you could renew at any consulate but they changed it so you could only renew in your home country.