Does your laptop have the original Apple SSD or was it replaced with a third party SSD? A third party SSD requires booting into macOS 10.13+ in order to be able to see & communicate with a third party internal SSD.
You can try booting into Internet Recovery Mode using Command + Option + R, but some Macs may still only boot to the older online installer for the version of macOS which shipped with the computer from the factory. And if this laptop has a third party internal SSD installed, then the older installer is too old to work with that third party internal SSD.
If you have access to another working Mac model generally from Late-2009 to mid-2020, then you can use it to create a bootable macOS USB installer.
- macOS 11.x -- a Mac model from 2013 to mid-2021
- macOS 10.15 -- a Mac model from 2012 to mid-2020
- macOS 10.13 -- a Mac model from Late-2009 to 2018
If your laptop has an original Apple SSD installed internally, then you could also use:
- macOS 10.11 --- a Mac model from 2007 to 2015
You can confirm the other working Mac is compatible with OS by using the information in the following article (the other "working" Mac can currently be running any version of macOS):
https://eshop.macsales.com/guides/Mac_OS_X_Compatibility
Just curious why you were wanting to perform a clean install of macOS? If your computer was having problems, then those same issues could be why you are having trouble reinstalling macOS. IIRC, some 2013 laptops had SSDs that were known to fail (Apple had a small free SSD repair program for a while) so perhaps the Apple SSD is failing or has failed completely.