Companies House applies the following:
- paging of results
- limits to the highest result you can request
- rate limits (on number of requests you can make in given time)
… to manage the amount of data (or rather capacity) that people can use. They have repeatedly stated that the purpose of the API is not bulk downloading - if you want to obtain larger quantities of information do that there are other means available.
Having said all that - the Advanced search endpoint uses paging (as do several of the endpoints). You can try increasing the size parameter. Depending on how many results you get back (you should count the entries in the items member the start_index can then be used to page through the data set (e.g. first page of 50 results would be (size=50, start_index=0), next page size=50, start_index=50 etc.)
See the documentation here:
For more general information on paging see here and the links from it.
https://forum.aws.chdev.org/t/searching-using-curl-returns-only-20-results-a-page/1454/2
Hope this helps. (PS. no need to post your API key here - you should keep that secret. Nor all your code…)