Etheiy

Hi, when I'm trying to create typographical art, especially things I want to not have that pixellated 'stair' effect, I typically stick to vector objects.

So I would use Designer, and each letter would be a vector object - that means that I can export it really big or really small and the software will handle the pixellation.. This way if I want to export it as a 120x120px JPG it will export alright, but if I ALSO want to export it as a 1200x1200px image it will be okay (no huge oversized pixels!).
Using vectors also means when I copy the letters and change them to pink in order to get the shadow, I can easily edit the 'nodes' of the pink version in order to give the appearance of a three-dimensional object (making the corners connect).

For example, I've quickly redrawn your 'F' below.
Using the Pen tool, I redrew the F shape as a vector (1 and 2)
Then I copied the F and made it pink, and put it behind the green one (3) which as you see, doesn't make them look connected or three-dimensional like in your example of what you wanted to achieve. We can fix that really easily with vectors.
Next I use the Node tool (4) to edit the nodes (the corners) of the pink F. I added nodes by clicking on the lines between them (my screenshot tool wouldn't pick that up for some reason, sorry) and then dragging the new node so that it snaps to the corner of the green shape (5)
I made this vector file at 600x600px and then exported it as a 120px jpg and a 1200px jpg, both attached. You can see that they both have pixels (as JPG is a raster format) but that these pixels aren't hugely obvious when the file is effectively scaled up by double the original size, and also that when I exported the tiny version, the export itself handled all the blending of colours to try to keep the edges looking somewhat true to the original. Of course, the smaller the export, the more obvious the pixels will be, and very small images have a lot less pixels to work with, so you lose crispness.

I hope this helped/wasn't too simplified (I have no idea how familiar you are with vector objects or affinity designer so I went with explaining what I needed to know when I started using them a few years ago).
I really like using vectors because I never really have to worry about my working file's resolution/size. I can export an A0 from a 600px file and it usually turns out just fine. It was really useful in my studies - before I started using vector graphics, I would have to work with high resolution raster (pixels) images and it would be very slow work because of all the extra information the computer had to hold on to, whilst with vectors it is much faster and scales well.
 

I don't know if this will help, but I found a solution last night where I exported all my pdfs from Designer, again, and updated the links in the Publisher document. I made sure that the color profiles matched the exports as well, meaning that when I exported the pages from designer I made sure to export them in RGB since that's what I needed on the export. This has never been an issue before and I hope it was some weird glitch, but for the time being re exporting all of my pdf files and then updating the links in Publisher solved it.

Are you able to export a non blank pdf if you don't rasterize it? Rasterizing seemed to be the main issue for me for some reason.

Another +1 for this feature. 
 In my architectural presentations/portfolios I tend(ed) to use a no-print layer with notes for what I needed to talk about on that 'slide' on it, or notes about possible rearrangements of images if I was printing to then cut+mount. This way near deadlines, if I'd been up for three days running on caffeine and anxiety, there was no chance I'd print out my notes to self. I always have a 'no-print' layer or two in my CAD files too, which I use for construction geometry and notes and reference drawings - that way I can see them and snap to them but they won't print even if I forget to turn them off...  I didn't realise this wasn't, well, a standard layout feature until just now - I'm putting together a presentation on my first project for my MArch! I've only used InDesign (in terms of dedicated print layout software) prior to using Affinity Publisher, though. 

did you try the same with the move tool?

I'm not sure if this is the right place to put this, but I simply had to stop my work and give all of you there at Affinity a huge thanks! I have used your products for years, but this ability now to switch back and forth to use various tools in each of the three programs is beyond anything  I dreamt of in the past. I am working on a book project with tons of complex graphic, I have made - yes, brought over from Freehand and Illustrator but in Designer since it came out. To switch back and forth in Affinity's programs saves tons of time and frustration. All I can say is "Bravo!" for thinking of us who work day and night in publishing. Your work is appreciated far beyond these few words.