Sorry, that's just not how sync works -- it syncs all files so you can access them at any time.
Is this just a money question or do you have other reasons you don't just want your files to sync when you add them?

You can't pick which files you want to sync and which you want to keep local only. If free tier is enough for you, then it's best to just sync everything.

Attachments are not automatically downloaded on iOS devices, so if you just want to read some specific documents on your iPad, you can download only those. On iOS there is a filter for "Downloaded Files", so you can see which attachments are downloaded on device.

If, for some reason, you really want to keep sync off for most items and attachments and only sync some specific items, I can see one solution. You could create a private group, then disable sync for "My Library" and enable sync for that new group. Then you can move items which you want to sync to that group. That way only that one group would be synced while keeping everything else local to your PC.
However it can be dangerous and I don't recommend it. If something happens to your PC or you delete something by accident, you'll loose it forever. If it's synced to our servers you can always retrieve your data.

Not sure what's strange about this -- the basic idea is that you sync your entire library and then have it available wherever you go (as long as you have internet access), rather than having to decide on the exact reading list for your (say) flight in advance.

And this isn't actually the case:

And I can't just "sync everything" because I have like 5GB of attachments.

You can absolutely sync 5GBs of attachments; many people do. That's why I was asking whether this is about money or some other concern. If you can spend $60/year on Zotero, this will give you by far the smoothest experience.

For the group, I'd be a bit more weary about this -- moving items back to the library from the group is a mess and if you do you that'll break the connection to references in any Word docs that you have inserted, so I don't think it's a great workflow. But if you really want to use it, disable file sync for My library in the Zotero prefs, then use the purge storage function for My Library on https://www.zotero.org/settings/storage, then set up the group.

I don't download every show to watch when I am on the go, I don't have all my music on my phone, I don't have every podcast I follow downloaded etc...
Seems more logical, as space on devices is limited.

And as explained above, you don't have to have everything on your device. Everything gets synced to the online library, but by default the app will only download the files you open. But the point of syncing is make everything available from any device, whether or not it's downloaded.

This is getting dumb. If you're out of space, obviously you won't have all your files everywhere, because you're not actually using file syncing. We're explaining to you how syncing actually works when you're using it, which is also how essentially every cloud storage service works: everything in the cloud storage folder is available online, but you can choose what to download to a given device.

The way you've decided it should work is not relevant here. It would be confusing and error-prone and cause people to not be able to access files when they needed them and lose large portions of their library when their computer crashed, and we would never implement something like that.

If you don't want to pay for a subscription, you can use WebDAV. But one way or another, you need space for all your files.

Just to clear it up a bit, above you mentioned: "I don't download every show to watch when I am on the go, I don't have all my music on my phone, I don't have every podcast I follow downloaded etc...". You probably mean services like Netflix, Spotify and similar. They have their own online libraries of shows, music or podcasts, which they host on their servers and you download which ones you want to consume.

But Zotero doesn't work that way. We don't have our own library of PDFs which you download. You create your own library of articles, PDFs or other items, which gets uploaded to your Zotero Storage or WebDAV (depends how you set it up) and then you can choose on your devices which attachments you want to actually download and carry on that device.

So saying you don't know which files get synced and free storage is enough space for you (but then suddenly you don't have enough space) is just misunderstanding the foundation how Zotero works. You apparently have a slightly bigger library (5+ gigs from what you wrote) and free Zotero storage plan doesn't cover that, so your files stopped uploading to our storage and you couldn't access them from other devices. If you would have bought more storage or set up your own WebDAV you wouldn't have any problems.

Anyway if you're fine with the solution above, that's ok. Just bear in mind that if your computer breaks or you delete something by accident, we won't be able to help you get them back. Those files are not stored on our servers, but only on your computer.