MacBook can no longer find Time Machine backup disk

It's clear that Time Machine on MBA2 is somehow not talking successfully to the NAS.

Agreed. But MBA1 appears to be backing up ok...?

If MBA2 is stuck in the "Preparing..." stage, let it continue. I realize not seeing any apparent progress is frustrating, but give it at least a day or two. Draw no conclusions until it reports a failure.

Excerpted from If Time Machine remains in the preparing stage on Mac - Apple Support:

The preparation stage can also take longer if:

• ...
• A software update was recently installed.

... which is certainly applicable.

You might want to contact Synology before doing anything else.

Personally I gave up on Synology's ability to reliably back up or restore with Time Machine years ago. They were unable to fix it and kept insisting I was must be doing something wrong, and when they couldn't identify what that was, they insisted there must be something wrong with my network. When I showed my network could not possibly be any simpler they insisted Apple was doing something wrong with Time Machine. They essentially pointed fingers at everyone and everything except themselves. So I returned the NAS for a refund and never looked back.

I know Synology's NAS devices work for some people though, so perhaps things have changed since then.

"best NAS for Time Machine" round-ups from popular Mac sites, ...

... are all advertisements. They don't have to say they're advertisements. There is no truth in advertising clause for the Internet.

I'm not saying a Synology NAS won't work. In fact they do for a number of people, but there are too many variations in network topology and macOS versions to conclude they will be reliable for you when you really need it. I proved to myself (and to Synology, apparently) that it could not be relied upon in the dire circumstances in which it would be required to work.

No one will care about your data as much as you, so you have to find a solution you can confidently rely upon. For me it would be "anything other than Synology"... but as I wrote, that's just me.

Sounds plausible... but Time Machine does not itself impose such a limitation. I have many Macs backing up to many different Time Capsules, some of which are certain to back up to the same drive at the same time. I never experienced a single instance of a failure to back up or restore.

My eyes glazed over reading that thread. Yikes. There's no way I would have the patience to do any of that.

Definitely contact Synology. For all anyone knows they already have a fix in the works, but they won't know unless you tell them.

John Galt wrote:

It's clear that Time Machine on MBA2 is somehow not talking successfully to the NAS.

Agreed.

I take that back. If MBA2 is in the "Preparing..." stage that means TM found the backup image and is busy with its housekeeping, which will take a long time.

I am concerned about the apparent disagreement regarding available space, but leave that concern aside for the moment.

Thanks for all your input. I appreciate it. In the end I deleted the existing backup and started a new one, which is running successfully now (6% into the backup).

Hopefully that backup finished by now.

MBA1 was backing up fine. I backed it up before updating to Sonoma, and backed it up again post-Sonoma. MBA2 was backing up fine until ~10 days ago. I've had similar issues before, where TM to the Synology works fine for months and then one day just falls over, necessitating creating a new TM backup.

That experience mirrors mine with Synology. Back when I was trying to make it work years ago, the particular problem would manifest in an inability to restore a backup. Everything would appear to work fine, but during disaster recovery testing it would repeatedly fail to restore. A number of users on this site complained of the same, and there were many, many proposed fixes not unlike the ones you described on that Synology community support forum. I too tried a number of them, but given TM's "mission profile" I lost confidence in it and determined it was unsuitable for such a critical task. As I wrote it's your data, and no one cares more about it than you.

After so many years I was hoping they would have fixed it by now 😕