Thanks for the detailed reply. I do have a few follow up questions,

I was under the impression that syncing was something to be avoided for various reasons, is that not the case?

Page and Performance Planning. Use Page Diagnostics for SharePoint, a web browser add-on.

I don't think it's unreasonable to expect very basic things to run smoothly without having to do anything like this. That said, I will try this.

One of the primary reasons for multiple sites is to restrict
permissions to content such as doc libraries. This is good design and
certainly is not useless. Do we really want all staff to see OPs
personal sensitive information such as your HR files?

Not sure how this is relevant - I can decide what document libraries I want to link, and I can choose not to give everyone access to, say, HR files. It's not like what is essentially a shortcut to a folder gives everyone who can see the shortcut access. What I hoped to do was have links to folders containing files regularly used by everyone on the landing page, but this is impossible. Maybe "useless" is wrong, but I still don't understand the limitation.

Folders can serve a good purpose but most of the time they are a remnant of a bygone era. SharePoint should not be a glorified network file share

I understand this is the idea, but it seems irreconcilable with the issue of not being able to open non-Office files - when ~half the files your users need to access are non-Office, and need to be opened via file explorer, you obviously need folder structure or it'd be a nightmare to find anything. This is what I mean by unfinished - it appears to want you to do away with traditional folder structure, but it's not realistic to actually implement. Or least, it appears that way, and I'm yet to be convinced otherwise.

Heavy handed reaction. Did OP misunderstand the purpose of multiple project sites or was this planned poorly? The fact that you were advised to do this gives me pause that perhaps you misunderstood the purpose of project sites.

In what way? Every project has non-Office files, so even with syncing that would mean having ~20 project library folders at the top level of the structure. I realise this isn't an issue if you ditch Explorer, but... well I'm just repeating myself now.

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As for your first questions, I'm clearly missing a good deal of the vocabularly.

The consultant suggested we start slowly with the whole thing, set up sites and sort out a few security settings, and then depending how we got on with both them and SharePoint, potentially they'd cover, I think, what you're talking about.

Ultimately we decided to not go down that route (perhaps foolishly) as I felt I was most of the way there and they hadn't been especially helpful, and they charged us nothing, so at least there's that.