Invoke-PnpSiteTemplate infers that you are applying the template to the top level site and not the site you connected to.

[CyberneticNomad-v808]

Connect-PnpOnline -Url "https://tenantname.sharepoint.com/sites/sitename -Interactive -ClientId <ClientID> Followed by: Invoke-PnpSiteTemplate -Path .\TeamTemplate.pnp

The progress bar states that I am updating "https://tenantname.sharepoint.com" and doesn't mention the name of the site. This led me to believe I was modifying the top-level site for the entire company, not the one-team site.