Field boost vs query text boost

In elaticsearch7.x either of these queries are not working please correct me where i'm wrong.

i want a search which is boosted with field and specific word in a query.

query = ("winter foxˆ2" OR "summer ice")

query = ("winter fox"ˆ2 OR "summer ice")

   "query" : {
                     "bool" : {
                                    "must"   :[
                                            {
                                        "query_string" : {
                                                "query" : query,
                                                "fields" : ["field1^4", "field2^3",'field4^2','field3^2'],
                                                "quote_field_suffix": ".keyword",
                                                "default_operator": "OR",
                                                "type":"most_fields",
                                                "tie_breaker":1,
                                                "auto_generate_synonyms_phrase_query" : True,
                                                "phrase_slop" : 2
                                                 } 
                                             }

                                        ],


                                    },

                                }

To answer this it would help to understand what's not working.
Do you get an error when sending the query? If so, please include the exact JSON query and everything you can gather arount the error.
Or are you not finding expected documents, or the ranking is not as expected? Then please inlcude a small example of documents you have in your index and state which ones you expect to find or not find, and whats wrong with the answer you're getting. This will help others to answer to your problem.