Sendmail and DKIM for bounce messages?

I believe this has been discussed here before, but I am unable to locate
any pointers, and apparently my google-fu is lacking here.

We have servers which send out emails using a client domain: clients
have set up SPF records that allow us to do this, and DKIM keys have
been set up so our Sendmail/OpenDKIM smarthost setup can sign the
messages correctly. When mail gets delivered normally, everything is OK.

However, there are issues when message bounces are generated for our
smarthost, and it tries to deliver it to the sender the customer used.
Apparently, the setup I currently have does not DKIM sign messages where
the sender is the classic email bounce empty sender <>

This means that messages will languish in the mail queue for days if the
client's email systems (typically M365, Google or some such large email
handler) will not accept them, and then cause double bounces.

Is this just some configuration option I need to change, or what?
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