In term of performance, is there any difference between using synonyms_path and using synonyms when specifying synonym filter for Elasticsearch ? Please refer to the images
You don't have a choice then since you cannot use a synonyms file. Your only choice is to provide all the synonyms in the index settings.
Code-wise, whether the synonyms are read from a string or from a file, it makes almost no difference. The only difference will be that all the synonyms will be stored in all the indices that need them, so that boils down to wasting a bit of storage space, but that's negligible (of course it depends how many synonyms you have, i.e. a few hundreds or many thousands).
What hurts more is that if you need to modify the synonyms list, you'll need to modify all your indices, instead of just a single file.