Once a branch in another state is established, it would be considered as an establishment for the purpose of GST. And as the limit of Rs. 20 lakh is PAN-based, registration would be required in such state. Please refer to Section 25(4),(5),(8).
Also, where work is performed in such other state, and goods/consumables are purchased with GST, such ITC cannot be claimed in the other state. Therefore, it would be beneficial to register in such state, claim eligible ITC.