firstname.lastname@gmail.com and firstnamelastname@gmail.com are the same address, according to gmail documentation. If this is what is actually happening (and there isn't a subtle typo, etc.), then something is more wrong than "wires crossed" & you should report it as a security vulnerability.

https://support.google.com/mail/answer/7436150?hl=en#:~:text...

https://www.google.com/appserve/security-bugs/m2/new