Because I like projects logs with pictures, here we go:

Photo of display and battery with third object for scale. I thought of using banana for this, but settled down with 555 timer in DIP-8.

Those components are really tiny.

By the way, notice the connector on battery.

Sellers usually don't care and call it JST connector, though it isn't real JST. In fact, it has 1,25mm pitch and belongs to Molex Picoblade series. The exact part number for my application is Molex 0530480210. I bought it here though it is available at mouser or digi-key.

By the way, PCBs are ordered and I should receive it during next week.