I can't reinstall Ventura, it says not enough storage, but my disk is nearly empty

"Other" (or System Data) does not necessarily mean disk volumes, but is a "catchall" category for various macOS system processes. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins.

Ref: What is “Other” storage on a Mac, and how… - Apple Community

One of the items, temporarily stored in Other, is Time Machine local snapshots. They can take up a considerable amount of space. These are very common with Mac laptops as you typically do not have a destination backup drive attached for the hourly backups ... so they can build up over time ... even if they do get purged by macOS periodically. You may want to verify their existence and manually delete them to make additional storage space for the Ventura installation.

There are a number of methods available to you to do so:

• The easiest, but not always successful, is to temporarily disable TM's "automatic" backups. Leave it disable for 15-30 mins, and then, re-enable it.
• A little bit more difficult, would be a series of commands that would need to be entered into the Terminal app.

Ref: About Time Machine local snapshots - Apple Support

Reinstalling the system won't necessarily increase system performance if you use migration assistant to reinstall all of your apps and data because you could have some software installed that is causing the problem. it's best to try to determine cause of the program first. With that in mind:

Download and run Etrecheck. Be sure to give it Full Disk access before running.

Copy and paste the results into your reply. Etrecheck is a diagnostic tool that was developed by one of the most respected users here in the ASC and recommended by Apple Support  to provide a snapshot of the system and help identify the more obvious culprits that can adversely affect a Mac's performance.

Copy the report

and use the Additional Text button to paste the report in your reply.

Then we can evaluate the report to see if we can determine the cause of the problem.

1. Check Application Size: Make sure that the size of the Ventura application and any associated files or data do not exceed the available storage on your disk. Applications can have multiple components beyond just the main executable.
2. Temporary Files: Sometimes, temporary files or caches can accumulate and take up storage space. Try clearing temporary files from your system using a cleaning tool or manually deleting files you no longer need.
3. Check Storage Allocation: Verify that your computer is recognizing the available storage correctly. You can do this by checking your storage settings or using a third-party disk utility tool.
4. Check for Hidden Files: Some files might be hidden or stored in locations that you're not immediately aware of. Use a disk analysis tool to identify where the storage space is being used.
5. Reboot Your Computer: Sometimes, a reboot can help reset certain system processes and clear up any storage-related issues.
6. Install Location: Make sure you're attempting to reinstall Ventura in the correct location. If you have multiple storage devices or partitions, ensure you're selecting the right one.
7. File System Errors: Disk errors or file system corruption can sometimes lead to incorrect storage readings. Running a disk utility or checking for errors using the built-in tools can help.
8. Application Dependencies: Ventura might have dependencies or requirements that need to be met for the installation to proceed. Check if the application requires any specific software or libraries to be installed first.
9. Contact Support: If you're still facing issues, it might be a good idea to contact Ventura's support or customer service. They might be able to provide more specific guidance based on the error message you're encountering.

With Gigabit Internet, I would suspect that syncing should be relatively fast ... however, there are other factors that could be in play here.

That could be your local network, how you connect your mini to that network, and/or the mini itself.

One great troubleshooting app that many of us recommend here is EtreCheck. It was developed by a fellow forum member and comes in very handy to pinpoint potential issues with your Mac. I strongly suggest that you consider getting it and posting its resultant report if you want assistance with interpreting its results. You may be surprised on what is uncovered, even if your Mac is running well.

FWIW, I only get a "blazing" 40 Mbps Internet connection here and my (current) M2 Pro Mac mini is not having any issues with syncing with Apple iCloud apps, including the Photos app ... and syncing in short order. I do connect by mini by Gigabit Ethernet to my local network vs. using Wi-Fi.

I honestly can't say if EtreCheck specifically calls out Private Relay, or its potential performance impacts. I personally don't use Private Relay. Have no compelling reason to at this point in time. I run a local network, based on UniFi products, and have implemented a pfSense firewall appliance to augment it. However, my computing/networking goals may be vastly different than yours. Fiber is just not an option in my local ... at least for any foreseeable future.

MiniMe2 wrote:

I found a setting in the Messages app, on the iMessage tab, called "Enable Messages in iCloud" that in its default value ("off") prohibits iCloud syncing even if you are logged into iCloud.

Correct, that would enable/disable syncing the Messages app data to iCloud ... not affect other iCloud apps syncing. As you know, you control which apps get synced via System Settings > Apple ID

... and you can let Apple know directly here: Product Feedback - Apple

MiniMe2 wrote:

I'm not afraid to download etrecheck, it's just that there's no reason to use it now. If you've ever run etrecheck on a new M1 Mac mini, you already have the same results that you would see if it was run on my Mini. Right?

One of the best troubleshooting steps is to have a ready baseline of your Mac BEFORE it experiencing any issues. Running an EtreCheck report with a "fresh" macOS install, would provide you with that baseline. However, it's totally up to you.