I am assuming that you have your custom column added in the database and custom field present on the admin company edit page in the General section.

1. For reading the column value from the database into the field on the admin page:

Add in di.xml:

<!-- override core class in order to have the custom column show on the admin company edit page -->
<preference for="Magento\Company\Model\Company\DataProvider" type="MyVendor\MyModule\Model\Company\DataProvider" />

And in your DataProvider.php:

namespace MyVendor\MyModule\Model\Company;

class DataProvider extends \Magento\Company\Model\Company\DataProvider {
    
    public function getGeneralData(\Magento\Company\Api\Data\CompanyInterface $company) {
        
        $result = parent::getGeneralData($company);
        
        # add custom column value to the General data section so that the value populates the custom field on the admin company edit page
        $result['my_custom_column'] = $company->setMyCustomColumn();
        
        return $result;
    }
}

2. For saving the field into the database custom column:

Add in di.xml:

<!-- override core class by plugin in order to save value from the admin company edit page into the custom column my_custom_column -->
<type name="Magento\Company\Model\CompanyRepository">
    <plugin name="myvendor_mymodule_after_save_company" type="MyVendor\MyModule\Plugin\Model\CompanyRepository" />
</type>

And in your CompanyRepository.php:

namespace MyVendor\MyModule\Plugin\Model;

class CompanyRepository {
    
    public function afterSave(\Magento\Company\Model\CompanyRepository $companyRepository, \Magento\Company\Api\Data\CompanyInterface $company) {
        
        $my_custom_column = 'some value here';
        
        $company->setMyCustomColumn($my_custom_column);
        
        $company->save();
        
        return $company;
    }
}

I am assuming that you have your custom column added in the database and custom field present on the admin company edit page in the General section.

1. For reading the column value from the database into the field on the admin page:

Add in di.xml:

<!-- override core class in order to have the custom column show on the admin company edit page -->
<preference for="Magento\Company\Model\Company\DataProvider" type="MyVendor\MyModule\Model\Company\DataProvider" />

And in your DataProvider.php:

namespace MyVendor\MyModule\Model\Company;

class DataProvider extends \Magento\Company\Model\Company\DataProvider {
    
    public function getGeneralData(\Magento\Company\Api\Data\CompanyInterface $company) {
        
        $result = parent::getGeneralData($company);
        
        # add custom column value to the General data section so that the value populates the custom field on the admin company edit page
        $result['my_custom_column'] = $company->getMyCustomColumn();
        
        return $result;
    }
}

2. For saving the field into the database custom column:

Add this code in di.xml:

<!-- override core class by plugin in order to save value from the admin company edit page into the custom column my_custom_column -->
<type name="Magento\Company\Model\CompanyRepository">
    <plugin name="myvendor_mymodule_after_save_company" type="MyVendor\MyModule\Plugin\Model\CompanyRepository" />
</type>

And in your CompanyRepository.php:

namespace MyVendor\MyModule\Plugin\Model;

class CompanyRepository {
    
    public function afterSave(\Magento\Company\Model\CompanyRepository $companyRepository, \Magento\Company\Api\Data\CompanyInterface $company) {
        
        $my_custom_column = 'some value here';
        
        $company->setMyCustomColumn($my_custom_column);
        
        $company->save();
        
        return $company;
    }
}