Hello @Sofiya Gubatska
Welcome to the Atlassian community.
I'm not sure what you mean by this:
"A bit of context: we’re using the standard Jira subscription, not the cloud version — the web one"
Jira Cloud is the software-as-a-service product offered by Atlassian where they host it and maintain the infrastructure. You can have a Free, Standard, Premium, or Enterprise subscription to that product. I'm not sure what you are trying to say with the statement that you use "the web one" but not "the cloud version".
Regardless, based on the screen image you presented you appear to be using Jira Cloud.
In what type of project/space are you seeing this behaviour? Get that information from the Type column on the View All Spaces page available under the Spaces menu.
In Team Managed projects the Resolution field will be set automatically when you transition to a status that is in the Done status category (has a green lozenge).
In Company Managed project setting the Resolution must be done either by showing the user a Transition screen where they are required to set the Resolution, or by setting it automatically as a Post Function in the Workflow. If you are not showing a screen to the user, then it is likely that the Post Function is missing from the workflow.
You will need to modify the workflow used in this project/space by the work item type to add the Post Function that sets the Resolution field, in that case.
https://support.atlassian.com/jira-cloud-administration/docs/configure-advanced-issue-workflows/#Use-a-post-function-to-set-a-field
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