There is no universal charger that can charge batteries with different types of contacts, like a particular Xiaomi phone battery, except one designed to have a cradle that holds that specific battery in the correct position to have contacts placed where the battery contacts are.
Why can't you just charge it in the phone, considering it is a cartridge style, not tethered by wire or ribbon to make the connection?
It is a little different for the battery with the JST connector, for it you can just get a hobby charger and make a cable for it that has the correct charger plugs on one end and the JST 1.25mm socket on the other end. Perhaps someone makes such a cable already or if not, just buy the connectors at an electronics supply house in your region and solder it together.