M1 mac recovery mode won't start (spinning flower)

Sounds like you booted with a thumb drive and erased the internal disk and planned to boot from the external drive to re-install macOS Ventura 13.0.1 clean. This will not work on M1 / M2 Macs.

Apple Silicon based Macs cannot be re-imaged in the traditional sense from a USB boot drive. You can boot from an external drive only if the internal drive is working and has the necessary special volumes. There are several technical reasons for this but the bottom line is the new security model doesn't allow it. Modern Macs rely on a chain of trust straight back to Apple.

In order to fix this problem you are going to need a second Mac and a USB-C data cable. On the second working Mac you install Apple Configurator 2 from the App Store.

Then you put the broken Mac into DFU mode ← [click link]. It can take several attempts to get the Mac into DFU mode, follow the instructions from Apple on that link. The broken Mac will have a black screen but on the working Mac, in Apple Configurator 2 the broken Mac appears as an external attached device and you can then tell it to revive or restore macOS to factory conditions. You are certainly going to need to restore rather than revive. Apple Configurator 2 will download Ventura 13.01 and then install it onto the broken Mac.

If you don't have a second Mac available, you might need to bring the M1 Mac Mini to an Apple Store and they will do it for you. Or find a friend to assist you.

The right way to erase and Apple Silicon Computer is done via the Apple Support link in below

Use Disk Utility to erase a Mac with Apple silicon

Followed by the Apple Silicon Method in the below link

How to reinstall macOS

Do otherwise as my learned colleague posts out rightly may required the use of Apple Configurator for Apple Silicon computers

Outside of these method not work >>

Have the computer evaluated by the Professionals who have the Special Hardware / Software and Expertise to diagnose the issue and offer possible solutions

How was this Erasure of the M1 Mac Mini attempted and details are important.

If done incorrectly it could be problem