I went a bit off track with this comment. So upfront I'll say that an iPad and an Apple Pencil is required to make the most of this app. The macOS app is not yet as polished as I'm certain it will get, and the iPhone app is ... severely lacking. (Erm, very focused on what it does?)
Having briefly played with the iPhone, macOS and iPad apps today for the first time I can definitively say:
1. The iPhone app is confusing - especially when syncing for the first time. There are zero controls, you can't sign in or sign out, and it's not even clear how the app works. The iPhone app lets you collect inbox items, then you can drag them out on an iPad or Mac to a particular board later. But it only synced/kept the items I added after I set up an iPad or macOS app. In fact, items only synced after I set up my iPad. (Which was odd.)
2. The macOS app has weird jerky behaviour when scrolling using a magic trackpad where it tries to "stop" at the right points when I kind of just want to smoothly navigate. The same isn't true of the iPad version, or at least the iPad seemed to perform buttery smooth in general.
3. I created a new board on the macOS app and it didn't seem to prompt me to name the board. I right clicked and renamed the board and the UI that showed up was very ... iOS-like? Big fat modal, tiny input in the middle. Not what I expected. Then I added the name, and it didn't show up until I entered the board then exited the board and maybe resized the board.
4. I went to my iPad after using the app on my mac and the items on the board hadn't resized themselves correctly. They moved - yes - but not perfectly. I had to resize and place items again, which felt a bit odd.
5. I wanted to expand the canvas to the left, and couldn't, because the canvas apparently only expands to the right or bottom of the screen. Okay, but then selecting everything on the Getting Started board and moving it to give myself extra space on the left is both annoying and somehow super-slow to finish redrawing/saving. Perhaps this isn't that noticeable because selecting everything is a simple shortcut on the Mac, but isn't frequently/easily done on iPad.
I actually have a renewed appreciation for apps like Obsidian and Craft and Notion because for all the rough edges (and there are often a lot with these kinds of apps!), they really do "just work" pretty darn well.
I think the app closest in spirit, if not in implementation, might be OneNote, with how you can make and drag text blocks and scribble notes with ink and so on. Obviously Muse has the concept of "infinitely nested boards" but I'm not actually sold on it as a replacement for tagging or infinite canvas. If you can't fluid zoom, you're navigating between "pages" but making me think about where I've placed each page's content within its parent, which is a bit strange. It's like having Finder stuck in "Icon view" and no way to set it to "List" or "Detail" view to sort or browse as I please. I enjoy not having to think about tagging or hyperlinks, but ... I also don't have those features either. Snipping of a PDF or image and seeing the larger view (in context) is great, but the alternative I used to use was to use OneNote's PDF Printout feature, and then when later referring to a slide, I could link to part of a OneNote note to go back to it in the source doc.
I actually don't like/use OneNote often because the interface is so different on every platform and because its feature set needs to keep up with the times. For example, a standout feature of OneNote was that it would perform OCR on images and you could search images for text. Cool. But an M1 MacBook or iPad now does that "for free" and as a bonus, you can select text within the image as if it were actually text (something that OneNote never offered unless you converted or extracted the text from the image) and I think it does column detection and so on, like Preview did for PDFs.
I'd really like to see Apple come up with a generic way to embed snippets or previews of documents in other documents. Bonus points if they can find a way to enable "live editing" like Adobe or Microsoft do in their suites, such that from right inside a macOS app that I've embedded an OmniGraffle diagram, say, I can edit the diagram then finish and go back to the app it is being displayed in. Kind of like how if you edit an Excel file in Word, the UI suddenly changes to Excel, but then you stop and it goes back to Word again.
Is it hard? Yes. Would it probably require a lot of transparent layering to make this work? Yes. Would it be absolutely awesome? Yes.
The way I see it, some apps do outlining really well, some apps do spreadsheets well, some apps do diagramming well... I'd love to be able to embed and/or round-trip a screenshot to the original app and then back to a PNG or PDF export again, all without leaving the document or app it's being displayed in.
I know, I'm asking for Apple to reinvent Microsoft OLE. But they would do it better, wouldn't they? An advanced version could maybe work something like iOS Widgets, but should allow re-use of document edit views. Perhaps the auto-save dropdown could be re-purposed to include options for embedding files and showing the file size including embedded files, as well as listing each of the embedded files.
Anyway... not sure how I got to making a feature request to Apple here.
All I'm saying is Muse is pretty awesome, but it could be even more awesome. :)