Example projects are there, documentation exists, but no board definition for STM8S003F3 exists yet.
You would have to follow docs on how to create a board definition, e.g. based on the stm8s103f3 definition. If you have problems with that let me know, but basically copying that file as boards/stm8s003f3.json in the project folder and changing up f_cpu to 16000000L, mcu to stm8s103f3p6, maximum_ram to 1024, maximum_size to 8192 and the macro STM8S103 to STM8S003 should work. With that file created you can use board = stm8s003f3 in the platformio.ini of the project to use the file.
There’s also currently a caveat that the SDCC compiler packaged by PlatformIO needs to be exchanged for the current 4.0 version in order to successfully compile code on Windows (Error 309 - "arduino-fade-all-pins" for the platform "ST STM8" - #18 by vampir8).
For assembly, just try and put .S (or .s or .asm) in the src/ folder. PlatformIO should attempt to assemble these with the configured assembler, which is
and then link them into the project.