Backing Up A Mac Wirelessly. Is This Possible?

I believe you can use Time Machine with a network attached storage (NAS) device. However, as I don't do this myself, I'm not sure how well this works in practice or what specific devices are supported.

I use Time Machine with a Sinology NAS.

It's slow to backup over wi-fi, but has been relatively stable.

But, and it's a big “but”, I'm happy that I've never had to rely on it to recover data. I dread to think how slow the process would be for a system recovery.

My primary backup for that level of recovery would be the Time Machine backup I keep on an external SSD.

The NAS is simply there as a Time Machine destination because I have the NAS and have capacity. It's running all the time, so there's no harm in having my MacBook use it. The SSD is typically attached for weekly backups, so the NAS is there for any small gotchas that might occur `and where the NAS has the most recent backup of a file.

I doubt that I would recommend a NAS as the sole Time Machine destination unless you have very specific use case and needs. An SSD will be much cheaper, very much faster, and takes much less to setup and maintain. The only thing in its favour is that you can mostly “set it and forget it” compared to an external Ssd, which you have to remember to regularly connect.