If you don't want to use services like algolia and typesense and you don't need any ai prebuilt tools then i have one simple solution using list.
For this solution you have to add all words of your content what you want to search in list by splitting with space and keywords like the,a,is,with,etc unnecessary words and don't pass string in where query use splitted list with spaces and now you have to search from flutter firebase sdk like below 👇 code
_carscollection.where('wordlistfieldname', arrayContainsAny: carsearchquerylist);

Note: change wordlistfieldname with your array field name in firestore document, and use splitted list of search query string and pass that list in arraycontainsany

If you don't want to use services like algolia and typesense and you don't need any ai prebuilt tools then i have one simple solution using list.
For this solution you have to add all words of your content what you want to search in list by splitting with space and keywords like the,a,is,with,etc unnecessary words and don't pass string in where query use splitted list with spaces and now you have to search from flutter firebase sdk like below 👇 code
_carscollection.where('wordlistfieldname', arrayContainsAny: carsearchquerylist);

Note: change wordlistfieldname with your array field name in firestore document, and use splitted list of search query string and pass that list in arraycontainsany