The STM8S003 is almost identical to the STM8S103. The only difference I am aware of is the size of the EEPROM: 128 bytes vs. 640 bytes.

I am not sure why the '003 is sold for half the price, or, to put it the other way around, why anybody should choose the '103 at all. Did I miss an important difference?

All you have to do in order to develop for the STM8S003 is setting the board manager for 'Generic STM8S103 breakout board'. Just keep in mind not to use EEPROM locations above 127/0x7f.

All differences between the CPUs:

Feature STM8S003 STM8S103
EEPROM size 128 Bytes 640 Bytes

Known development boards

I am not aware of any dedicated STM8S003 breakout board, but this CPU is used in many other low-cost boards:

The stm8ef wiki lists more.