Make “Apply for this position” form optional

We don’t support the functionality to hide the job application form from WP Job Openings Settings. But, you can remove it completely if you follow the below steps:

1. Open your child theme functions.php file(We don’t recommend using your main theme file. Because, when theme gets updated, entire customization will be lost).

2. Add this code to functions.php file:

function wjo_remove_form_hooks() {
    if( class_exists('AWSM_Job_Openings_Form') ) {
        remove_action( 'awsm_application_form_init', array( AWSM_Job_Openings_Form::init(), 'application_form' ) );
        remove_action( 'before_awsm_job_details', array( AWSM_Job_Openings_Form::init(), 'insert_application' ) );
        remove_action( 'wp_ajax_awsm_applicant_form_submission', array( AWSM_Job_Openings_Form::init(), 'ajax_handle' ) );
        remove_action( 'wp_ajax_nopriv_awsm_applicant_form_submission', array( AWSM_Job_Openings_Form::init(), 'ajax_handle' ) );
    }
}
add_action( 'wp_loaded', 'wjo_remove_form_hooks', 99 );

I did as you suggested and everything has been working fine. But the website is now live and I received the following email from Google Search Console:

—————-
Search Console has identified that your site is affected by 5 new Job Postings related issues. This means that Job Postings may be negatively affected in Google Search results. We encourage you to fix these issues.

Top 5 new issues found, ordered by number of affected pages:
Missing field “baseSalary”
Missing field “employmentType”
Missing field “validThrough”
Missing field “hiringOrganization”
Missing field “jobLocation”
—————-

Since those fields are not used in our Job Postings listings, I think they must be associated with the application form which we’ve suppressed. How can I resolve this so that Google Search results will not be negatively affected?

I think they must be associated with the application form which we’ve suppressed.

No. These are not related to application form. These fields are related to Job Specifications(e.g. Job Type, Job Location) and some general settings(e.g. Name of the Company).
Google uses job posting structured data to display Jobs in search result rather than considering these as normal posts.
https://developers.google.com/search/docs/data-types/images/jobs-search-ui.png
This job posting data needs the above mentioned values. If you don’t fill these values your posted jobs may not correctly display in Google Search results. That’s it!
You can read more about this issue from this answer.