I renewed my sites' cert and it looks like all is good until June 10, but I am still getting email notifications that they are about to expire. Is this just a bug in the system?
The domain variants in the email seem to be the exact same as what I have.
Most often people don't realize a cert is only considered a "renewal" if it has the exact same set of names in the cert. If you add or remove names that doesn't look like the same cert to Let's Encrypt.
If you share the domain name(s) in question we can look at your history and help you. Or, use a tool like https://crt.sh and look yourself.
If you re-read the email carefully now it may make more sense. Also see
Is the email warning about the cert issued on Jan2 with 4 domain names in it?
Because after that date you got individual certs for your two base domain names. That is, cert for damnsmallinux.org and www in one cert and dslos.com and www in a separate cert. You also got one cert with only the dslos.com name in it so expect a cert expiry warning email for that too.