These three libraries are popular for your use-case:
If the database is local you can use Eloquent, If not, remote connection to that database may help. otherwise, if you only have API access you should consume eighter of above libraries or any alternative options to make an HTTP request your application might require.
Security-wise, as long as you are only making a request to a remote server, the Suggested way is to store any key or secret string related to authorizing your request (if applicable) in your .env to prevent it from committed to your version control systems. Needless to say to always handle any possible HTTP error your remote API might throw in order to prevent any unwanted error on your application side.
And as Abir Adak mentioned in the comment check this thread for further details.
Updated Answer: On the case of MODIFIED
part, generally you have 3 popular options,
This blog post is a detailed walkthrough written for Laravel
This one from Stack Overflow can help you with designing you API
This last one can help you to develop a widely accepted API response and endpoints by following its specifications.
GraphQL
Can save some time for developing your API, but I suggest to make sure that the consumers of your API are happy to use this option.
GraphQ
Laravel Package for GraphQL
If using Laravel isn't a must, and you are using PostgreSQL, you might want to look at Hasura as well.
SOAP
Have little knowledge on this option for Laravel, just know folks coding using C# and .net are happier to expose their API with this protocol. read more about it on WikiPedia
Postman is a great tool for testing your API or any other API.