Time Machine repeats "Disk you inserted not readable" in sleep mode, but reads it fine once awake.

Open System Settings and search for "Nap", click on Power Nap (energy saver) and turn off "Wake for network access". The feature used to be called Power Nap and it was designed to wake up from sleep, check email, receive messages, etc. It's not on long enough for the backup drive to fully wake up and it attempts to run a backup and fails. This should stop the activity during sleep periods.

EtreCheck Report observations:

• You have 4 external disks. Two different WD Passports, a Seagate BUP Ultra, and LaCie Rugged. he screenshot shows BACKUP and MACDATA volumes were not ejected. Looking like both the WD Passports are not ejecting properly. EtreCheck obscured the volume names as B****p and M*****A but that's clearly both WD Passports with the problem.
• WD Passport drives are notorious for having this problem and it's been observed with Big Sur, Monterey and now Ventura. They must be doing something weird in their firmware. Not seeing these problems with other drive manufacturers. Suggested fixes were to reformat these drives. That's not an option for most people. Some people said their cables were faulty but since both of your Passport drives are wonky, I doubt its both cables.
• But another fix is to turn off "Put hard disks to sleep when possible" as well as "Wake for network access". This might help stop the ejection errors. You can still sleep and test with these options off. You can also remove the WD Passports overnight and see how things go.
• I see a lot of mdworker stuff going on which is Spotlight re-indexing all the drives. You might want to put all 4 drives into the Spotlight Privacy setting to turn off indexing on these external drives. Then I would re-index the internal SSD and when that fully completes. Add one of the external drives back in to be re-indexed by removing from Spotlight Privacy and forcing a re-index in terminal using the mdutil -E /Volumes/Backup (mdutil -E /Volumes/MACDATA). You can check the status on either with mdutil -s /Volumes/Backup or mdutil -s /Volumes/MACDATA to see how the indexing is progressing and to tell when it's completed.
• You've got enough storage requirements to fully justify switching over to a NAS. It would allow for future storage expansion as well. The number one NAS is Synology. It uses open source Time Capsule emulation and works really well even for multiple Mac Time Machine backups. A more technical (nerdy) option is TrueNAS either DIY or purchase one pre-built. Synology uses BTFS but TrueNAS uses FreeBSD and ZFS which is more robust than BTFS and in my opinion is superior. Although both have a web console and are fairly easy to use. The Synology is worlds easier than the TrueNAS. Personally, I would switch to a NAS solution and use those external drives as additional less frequent backups and I would use CCC - Carbon Copy Cloner while using Time Machine to the NAS.
• If you do settle on NAS, make sure you use actual NAS hard disks. Ironwolf/Pro, HGST NAS, Toshiba NAS N300, etc. I would avoid WD Red, I've had bad luck with them lately. Do not use non-NAS drives and make sure they are CMR drives and not SMR drives. SMR drives are not well suited for RAID and will have endless problems. SMR is fine for a large storage cheap external disk. But they do not behave well inside NAS systems. Avoid any Green / Blue / Black drives from WD as well.

Best of luck in trouble-shooting the problem. Pretty positive the issue are those two WD Passport drives. I would replace them with a LaCie drive or start planning on a NAS. When testing, make one change at a time and be methodical about it. Take notes.

Wow... Well that's not good! What is your external disk make / model? It seems to be having issues being disconnected improperly over and over while the Mac sleeps.

Perhaps there's software in play like the stuff WD provides or the drive or drive enclosure needs a firmware update. Please download EtreCheck, run a scan and attach the report in reply. The report will provide all the technical details to see what software might be causing this issue. It does not list personal information only technical details. The author is a frequent participant in these forums the App provides instructions on how to share the report on these forums.

Until it is fixed, I would recommend that you unmount / eject the disk and unplug it from the Mac before you put the Mac to sleep. Re-attach it after you wake and start to use the Mac. Yes, it's annoying but not nearly as annoying as all those alerts! That will avoid the problem. I don't think there is a way to dismiss the warnings about the disk not being properly ejected. You might also wish to run a Disk Utility First Aid on that drive.

Just remember that NAS (network array storage) despite its use of RAID (redundant array of inexpensive disks) is not bullet proof and is not to be fully trusted as your only backup source.

Always have more than one backup. i.e. a local cloned copy that you update periodically using Carbon Copy Cloner (CCC) or a cloud backup with a service such as BackBlaze. Or keep your critical files in iCloud, OneDrive, Google Drive, Dropbox, etc. I tend to use iCloud because the cost is very reasonable. Although its nature is quite different than other Cloud drives. It is tightly integrated with macOS. If you need cross-platform operating system support consider one of the other cloud drive solutions.

Depending on how the RAID is configured you might have the ability to have one or two disks fail without losing data, replace those drives and the RAID array will rebuild (resilver) itself. However more disks could fail during that process and you lose everything. Or you might have a RAID that uses mirrored pairs and you lose both drive pairs in a mirror and then you lose the entire array.

Basically NAS / RAID is fantastic and most of the time it works very well and is very reliable. However, it can also experience a series of unfortunate events that can still result in complete loss of all data. Therefore you shouldn't trust it implicitly and always have additional backups of your critical files if you cannot backup the entire NAS.