Please provide a full example that (does not) work(s) by itself.
The above is not valid Python code, and the next line's indent is 1 as expected.. ;)

For sure :)

Here a working example code.

def some_function():
    id=1
    d="somestring"
    LINE_BREAK="\n"
    rendered_result = 'System_Boundary({id},"{descr}") {{'.format(id=id,descr=d) + LINE_BREAK
    return rendered_result

print(some_function())

If text is being added after the some_function method it will be indented approx. 58-60 spaces to right

Works for me.
Is the "{{" recognized as "pythonString" with your syntax highlighting?
This should take care of skipping it:

I think it s interpreted as a variable

even a simple S="{{" provokes a file indent on the next line

Appears to be an issue with your syntax file then.

Looks like it delegates to some other syntax maybe?
What does :echo reverse(map(synstack(line("."), col(".")), 'synIDattr(v:val,"name")')) display? (or zS with vim-scriptease)

if the cursors location is in the string with the two curly brackets it displays:
['pythonStrFormat', 'pythonString']

So that should be ok. But there's another method used to check/skip this after all.
Can you try #133, please?
What syntax plugin/file are you using?

I am using the configuration of https://vim.fisadev.com/ at https://raw.githubusercontent.com/fisadev/fisa-vim-config/master/config.vim

works great!

Cool!
Will have to check this with regard to slower performance now maybe (and adding a test), but good to know already that it works.