Protect support workflow against info-siloing in Slack

Why is this change being made?

As a quick solution for our discussion in gitlab-com/support/support-uploader#7 (closed), cc @ronanoconnor

How will this merge request impact page speed?

Minimally.

Does this MR meet the acceptance criteria?

Assign to DRI

• Did you assign this change to the correct DRI of the page or information you are changing?

Conformity

• Added description to this MR explaining the reasons for the proposed change, per say-why-not-just-what