How to separate meat from vegetables in a soup?
Since the intermingling of the flavors is what your soup is about, and you want to remove only some of the solids (the chicken), a metal insert or colander might be too cumbersome. 

Boil bags are what I’d suggest - cheap, disposable, and will allow everything to simmer together nicely. 

https://www.amazon.com/dp/B071RJTTXH/ref=cm_sw_r_cp_api_i_8SdHCbFWV2C0R