Note: I decided Emil would sense things before Observation Haki was explained in detail, basing it on one scene where Luffy ran blindfolded through a forest without bumping into each tree and rock (or I imagined it because I can't find a clip with this scene anymore). I know Observation Haki doesn't work like that, but I don't care; I like Emil being a little 'everyone knows something is impossible till an idiot who doesn't know comes around and does it.' She's exactly that: as a blinded child in distress who didn't exactly know how Haki was supposed to work, she developed it in a different direction.
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If someone asked Emil how she perceives the world, and she didn't feel like going into details, she would say something along the lines of:
Imagine that everything is made out of glass. You can see silhouettes of things and people, and you can see through them into great distances, but you have no idea what colours they are.
It's nothing like that.
I have a headcanon that Observation Haki does not always give feedback similar to vision. It's the most common one, but it can be akin to other senses as well. Some would 'hear' with Haki, some would 'smell' (I HC that Bepo's Haki is smell-based), and Emil 'feels'.
The feedback Emil gets from her Haki is as if her whole Haki detection range (~1.6km/~1mile radius) was her body and people and things pressed against her skin. She can sense shapes, motions and - to some degree - textures and temperature but no colours or patterns.
Furthermore, I headcanon that everyone's Haki falls somewhere on the scale from 'selfish' Haki that perceives 'danger to the user', to 'selfless' Haki that perceives 'emotions of others'. While most users fall somewhere in the middle of the scale, Emil falls far on the selfish spectrum.
That's how she's able to sense objects. While having next to no feedback on other people's emotional state, Emil is able to sense inanimate objects because - between her 'selfish' Haki and her blindness - everything can be dangerous. Everything is a tripping hazard. Everything can smack her in the face.
Emil’s unaware that’s the reason. It comes naturally to her and she has no sense how the ‘proper’ Haki is supposed to work.
Still, not everything is as easy to pick on. Emil has a couple of 'sensitivity layers' she can perceive practically at the same time and overlay them. In order from easiest to the hardest to sense (that's also the order she developed them in time):
- strong and/or hostile animate beings; living creatures are the easiest to sense and ones that pose danger doubly so. Emil gets a sense of how strong people are and how angry/bloodthirsty they are. A big, but calm dog that could body-tackle her if it wanted to would ping on her radar just as much as a bloodthirsty squirrel.
- weaker and/or calm animate beings no smaller than a hamster; living beings are inherently way easier to sense than inanimate objects.
- inanimate objects moving at speeds and/or hot; the faster something moves or the hotter something is, the stronger the sensation of 'danger' it gives Emil. Oddly enough, it doesn't matter whether Emil or the object is moving, making stationary objects easier to sense if Emil's running. The sense of 'hotness' not only lets Emil sense bullets or fire, but it makes forging and cooking easier as - over the years of working in the smithy and the kitchen - she learned to recognise how strong of a feedback she gets from various temperatures. It's not pinpoint accurate and she wouldn't be able to feel whether someone has a fever or not, but a difference between a 220C and 240C oven? Sure.
- sharp edges/points and massive objects; while blades are easy to understand for their 'danger' potential, this is also the category where trees, boulders, or walls are; the stationary but massive or sturdy objects, hitting which would probably be a bad idea.
- stationery, room temperature, inanimate objects; your everyday, normal objects; the smaller they are the harder they are to sense; the further away they are, the 'fuzzier' they get. At 25, with 17 years of constant use of Observation Haki behind her belt, Emil can sense in her 'default' focus and about 25m/82' around her objects that are about 5mm/0.2'' in size. Please note: she would have no problem with sensing a sheet of paper someone held up but would be oblivious to another sheet laying flat on a desk. Once multiple sheets of paper are stacked till they are like 1mm thick, she would notice it but remain oblivious to an eraser bits ball beside it which while perhaps thicker, is still way smaller.
- animate being smaller than a hamster; this one has plenty of overlap with the point above. A mouse will be easier to sense than a potted plant, but an ant will be harder than a stationary object the size of a ping pong ball. Because yes, Emil can go as detailed as to sense individual ants within her close proximity.
Note that those are layers for Emil's default sensitivity. Her Observation Haki has a range of ~1.6km/~1mile with people still noticeable at the edges (but no objects), and Emil can focus and sacrifice it for the detail.
This exchange allows her to use precognition. For each second of foresight, she sacrifices 3/4 of her range, up to 3 seconds. So, 1.6km for no foresight, 400m for 1 second, 100m for 2 seconds and 25m for 3 seconds. Furthermore, her focus with 3 seconds has to be so tight that even sneezing can throw it off, and with no distractions, she would struggle to keep it for more than a couple of minutes at a time.
By the way, this 1.6km radius range? There's a caveat to it in regards to sensing inanimate objects. While yes, the furthest point Emil can detect is 1.6km away, there has to be a continuous line through air or water for it to work. The line doesn't have to be straight; as long as it's unbroken and doesn't go outside Emil's range, she can detect inanimate objects with no issue. The content of an air-sealed container in her hands would be a mystery till she pops it open, but a pair of scissors in a room with a vent three blocks away will be within her 'field of vision'.
There's no such limitation for living beings; as long as they are not sitting inside other creatures, Emil can sense them.
Speaking about 'field of vision', that would be a good comparison on how much info her mind is getting and processing. Everything within her range is in her 'field of vision', but she's not paying attention to everything at once. Spikes of 'danger' are like sudden movements that draw her attention, but just because something is within her Haki range doesn't mean she paid attention at the time. Yes, Emil tends to sweep through and note changes, but she can still miss things if it's not her point of interest. Flicking her attention from one point to another doesn't affect her range, just as moving one's eyes doesn't change one's field of vision, just what bits are in focus.
Fun fact: Emil can lipread and follow people's hand and pen movements to 'read' what they are writing. It's not a skill inherent to her haki but something she learned on her own, the same way a sighted person can learn to lipread. For either of those two work, Emil has to pay attention.