Currently it's not possible to customers to see any logs of their webhooks being fired on JIRA. Providing users with a way to see those logs via the UI would help customers a lot when troubleshooting issues with their webhooks and diminish support load on requests for those logs.

Workaround

While not available in the GUI, it is possible to write a line to the log file when a webhook is attempting to send.

1. Visit Jira Admin -> System -> Logging and Profiling
2. Add logging package com.atlassian.webhooks

Now, 2 lines will be logged to the jira log (atlassian.jira.log) file in the JIRA_HOME/log directory. Example:

2021-04-09 09:50:10,432+1000 Web-Hook-Publisher-1 DEBUG admin 590x289x1 19qeghr 127.0.0.1 /rest/api/2/issue/SCR-5/comment [c.a.webhooks.plugin.PublishTaskFactoryImpl$PublishTaskImpl] Posting to web hook at 'https://webhook.site/testwebhook, body is:
    SNIP_JSON_BODY_HERE

2021-04-09 09:50:12,039+1000 httpclient-callbacks:thread-1 DEBUG anonymous     [c.a.webhooks.plugin.PublishTaskFactoryImpl$PublishTaskImpl] WebHook successfully sent

Therefore, these lines can be checked in log to determine when a webhook attempted to send

To make this logging persist past reboots, check article Logging and profiling