Is there a way to archive automatically all emails related to this specific mission in the appropriate subsite
try this:
- configure incoming emails in Sharepoint online like shown here: Step-By-Step: Bring Incoming Email to Your SharePoint Online Instance
- configure rule for incoming emails in your mail client (Outlook or similar) which will redirect emails related with specific mission (you may decide how exactly filter such emails. E.g. if email subject contains mission title) to shared mailbox created on previous step