Honestly I think you'll be happy either way. Synology is very very good at some things. And the software makes it very easy and approachable to spin up a lot of private cloud type stuff without a lot of technical messing around. That said, you will get more hardware/performance for your dollar with a PC server. You can go the DIY route, or if you don't mind a little more power consumption and want more performance buy a used Dell PowerEdge on eBay. Based on what you say, I think you'll be happy either way. The real value you get from Synology is their software. Their photo app is very wife friendly. And I don't think you'll find any serious restrictions with it, you get full root SSH access into the box.

So I guess my suggestion would be evaluate the photo management in TrueNAS versus Synology. You can spin up a virtual machine of TrueNAS on your desktop and play with it if you want. The only other gotcha is if you want Plex to do transcoding you definitely want the PC because you can throw in a GPU and accelerate that a lot.

//edit- the one other thing to mention is backups- Synology has GREAT backup software and it's free. Active Backup for Business will back up your desktop/laptop, versioned, deduplicated, very efficiently. And Hyper Backup will backup your Synology itself (or some parts of it) to the cloud, optionally with client-side encryption. I suggest Wasabi as the backend for that, it's only like $7/TB/mo. Or just get another Synology and put it at the house of someone you know and you have an instant offsite backup with no recurring cost.