How to save the custom field on the checkout page

I am creating an application (not plugin) to integrate with shipping companies. However, I can’t deal with one problem - custom fields. I created one and linked it to an order. How can I save something to this field? It is called custom_parcel_locker_field. The template in which I need to display this field is: storefront/component/shipping/shipping-method.html.twig.

Tried to insert something like this, but didn’t work:

<input type="text" name="customFields['custom_parcel_locker_field']">
<input type="text" name="custom_parcel_locker_field">

I would like to point out that this is an application, not a plugin. I know how to do it on a plugin, but I don’t know how I can do it for an application,