Can we use a webservice with Wordpress?

Question

I change the details with the new information.

Here is the situation: Our customers have Wordpress sites, they can customize it as they wish with the theme of their choice. Our customers were originally on another CMS with some features provided by an external webservice. My question at the beginning was, can we use an external webservice with Wordpress? The answer is yes, I know it. I even discovered through other forums and research the wp_remote functions. (request, post, get)

I made a Wordpress plugin, in order to have a solution whatever the theme chosen by the user. It is a search widget that will communicate with a specific function of the external webservice to receive the information that the client wants.

My question is now this: Once my plugin has communicated with my external webservice and retrieved the necessary information from the client. What do you advise me to do to integrate this data into the site? (To have a correct display on a page)

At first, I used the wp_insert_post function to add my search content as a post to the site. The display was fine, which is what I wanted, but the method of getting this result.... is confusing to me.

Thanks for your answers.