Will Office 2011 Excel files open and run on a Mac 2023 Mini running Ventura

Yes, the files will open but you will need a more current version of Excel (or another app) to open them.

Microsoft does not provide free upgrades between major versions of their Office products (unless you subscribe to Microsoft 365) and older versions of Office are not compatible with macOS Catalina, Big Sur, Monterey or Ventura.

If you have a version of Microsoft Office that is not compatible, you can either subscribe to Microsoft 365 or you can make a one-time purchase. See: https://www.microsoft.com/en-us/microsoft-365/mac/microsoft-365-for-mac

Or use the free and very good Libre Office https://www.libreoffice.org/

or the free Microsoft Office on the web: https://products.office.com/en-us/free-office-online-for-the-web

or Google Docs: https://www.google.com/docs/about/

or Apple’s Pages and Numbers