Why isn't new (erased/formatted) SSD showing anymore in Disk Utility (and can't install OS on it)?
I think you bought a NVMe SSD, did you ? What model is your new SSD ?
macOS High Sierra was the first to support NVMe SSDs, that would explain why El Capitan can't see yours.

You may want to try cmd-alt-R at boot in order to boot the latest macOS Recovery available for your Mac from the internet. It should be Catalina, which supports NVMe SSDs.