Adding a multiple-choice custom field to a Program, will make it inaccessible

Issue Summary

This is reproducible on Data Center: (yes)

There are reports from the field that after the upgrade to 9.7.1 the Programs inside JPO are throwing 404 errors and are inaccessible, I can replicate the issue on 9.6.0 by only adding a multiple-choice custom field to an existing Program.

Steps to Reproduce

1. Create a Program with 2 or more Plans
2. Create a custom field (multiple-choice) with 4 or more options
3. Add the custom field to the existing Program
4. Try to access the Program

Expected Results

As a Jira admin we expect to be able to add a custom field multiple-choice or continue using the existing Programs that are attached to this type of field

Note: Per the link below it should be supportable.

https://confluence.atlassian.com/jirasoftwareserver/configure-custom-fields-in-advanced-roadmaps-1044784162.html

Actual Results

The below exception is thrown on the screen (screenshot below)
Note: There are no entries on Jira log, only access.log will show the 404 error while accessing the /rest/jpo/1.0/customfield/getOptions endpoint

404

No response available.

===============
=== Request ===
===============

URL: /j960/rest/jpo/1.0/customfield/getOptions
Type: POST
Status: 404
Data: "{\"optionIds\":[\"10402\",\"10404\"]}"

===================
=== Client Info ===
===================

User agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/119.0.0.0 Safari/537.36
Local time: Wed Nov 22 2023 14:19:02 GMT-0300 (Brasilia Standard Time)

===================
=== Plugin Info ===
===================

Plugin build: 9.6.0

===================
=== System Info ===
===================

Jira Title: Jira
Jira Version: 9.6.0
Agile Version: 9.6.0

Workaround

The only known workaround is to remove the custom field causing the error.