This would be my suggestion as well. It will cover almost all of your requirements (not sure for the hardest nut butters), and takes up the least space which as you mentioned is at a premium. This one comes with a 3 cup processor and is well rated. If you are super keen on the nut butters you could also get a bullet type machine, which also have low profiles compared to a full blender or food processor
I mean like this Brevile Immersion Blender. It has a 280 watt motor, if you can't grind your beans with 280w, you have some tough beans. The only problem is that if you put too heavy a load on too light a motor, it burns out. I have a regular Oster blender from the 1960s (my mom's old blender) and it has 750w motor, that's surely more power than commercial grinders. You could buy an old blender on Craig's List for $10. Or you could just get a real grinder.
That is a Breville immersion blender. Looks like this one on Amazon: https://www.amazon.com/Breville-BSB510XL-Control-Immersion-Blender/dp/B004RF7QJW
For food processor, I went with the 14 cup stainless Cuisinart decades ago. As I did this, I cannot justify buying the new shiny Breville Sous Chef 16 Pro. As I bought it decades ago I expect it to last me the rest of my life. I have no idea how a modern Cuisinart lasts, I know their stick blenders always die 2 years into their 3 year warranty, that is when you find out that to get the warranty honored you have to pay shipping both directions which costs more than the stick blender on sale. My main uses are slicing and dicing after that I'd say puree. Wait I also like grating hash browns and cheese and sometimes veg for various things. Food processors are a great help.
If you can't get a Vitamix blender now, I'd go with a cheap Oster. Those Osters have always been very loud tanks for me. I'd get a https://www.amazon.com/Breville-BSB510XL-Control-Immersion-Blender/dp/B004RF7QJW before a Vitamix, you will get more use out of it most likely. Unlike the Cuisinart garbage stick blenders, the Breville endures all. The only thing I think is better is one of the big Warings (not the sell out garbage model Waring made as a cash grab) The garbage Waring lists one part number for their cheap commercial and that is for the whole unit, that means you cannot replace parts and that it is disposable. I'd give up my Vitamix blender before my Breville stick blender. The only complaint is its head is bigger than normal so it will not fit all the way to the bottom of a 32 oz glass.
Also remember: if you are strapped for cash, Craigslist is often much cheaper than black Friday.
I have that one too!
I'm baffled too, we bought this one a couple years ago and I kinda suspect the shape of the base isn't incorporating air properly into the emulsion. It's also an oval shape instead of most round immersion blenders I've used so I don't think that's helping:
https://smile.amazon.com/Breville-BSB510XL-Control-Immersion-Blender/dp/B004RF7QJW/
I had a few more close looks at the video and I think he's using this All-clad model:
https://smile.amazon.com/gp/product/B007R2E47Y/
I don't think wattage is everything, but it's interesting that the All-clad is a 600 watt model while the Breville is only 280 watts. Thanks for listening to me rant, props to kenji though for upping my cooking game in all sorts of areas since the pandemic started...
Looks like the Breville BSB510XL Control Grip to me: https://www.amazon.com/dp/B004RF7QJW/
I got this for Christmas one year and it's a pretty good multi-purpose tool. https://www.amazon.ca/Breville-BSB510XL-BREBSB510XL-Immersion-Blender/dp/B004RF7QJW