Hi @kmazurek,
Right now any user should be able to see Account Settings > Integrations > Incoming Webhooks once the webhooks are enabled by the System Administrator.
(Please note if you change settings via the Mattermost System Console instead of the gitlab.rb file, it is recommended you backup the Mattermost config.json file before updating or reconfiguring GitLab to avoid losing your settings).
Troubleshooting instructions are available in our documentation if you've lost your System Administrator account.