Does anyone know exactly what's the size of this battery's connector?  https://tinycircuits.com/collections/batteries/products/lithium-ion-polymer-battery-3-7v-40mah

I am looking for JST 2PIN 1.25mm spacing

Here are some example product pages for the type of battery connector and mating connector (both 1mm):

Battery connector: https://www.digikey.com/en/products/detail/jst-sales-america-inc/SHR-02V-S-B/759866
Mating connector: https://www.digikey.com/en/products/detail/jst-sales-america-inc/SM02B-SRSS-TB-LF-SN/926708

The connector is a micro JST SH while most LiPo batteries are provided with the larger JST PH connector

I brought some JST SH pigtail leads on amazon and used these to replace the original PH connectors