You are a mail server.

You get an email without a DKIM signature from me.

Is that because I do not use DKIM and do not sign my emails or because the message is forged and not from me at all?

You cannot tell. There is a single SPF record that you can look up to see if SPF is configured. It's just a TXT record on the domain. But there is no standard DKIM record. A DKIM signed email tells you what key identifier it used and you have to use that to look up the DKIM key at <key identifier>._domainkey.<sender domain>. When the email has no DKIM signature you cannot tell if that's because the sender domain does not use DKIM or if it does have a DKIM key record but it was not used, potentially because the email is forged.

Right. And if you mandate dkim, as seems to be the case with servers that demand dmarc, what's the issue? You reject the emails where dkim isn't set.

Or do you think it's critical to support mail that doesn't have dkim?