In terms of characterising magic-users, I agree that the way they see the world is an important cue.
One point to consider is whether it differs from non-mages. Is it a setting where everyone is aware of magic, spirits etc., but only a few learn to use magic? Do spellcasters have senses that other people simply don’t? Is their entire understanding of reality fundamentally different?
You talked a bit about what spellcasters pay attention to, such as the effort of spellcasting or nearby spirits. I think we can expand on this too, along the same lines as a skilled soldier being instinctively alert to surroundings, lines of fire, whether other people seemed to be armed, routes of escape and so on. So we might instinctively note the presence or absence of iron (blocks magic), amber jewellery (stores mana, probably a mage), or wand-shaped bulges in the sleeve. That beggar’s gait is the smooth glide of one used to floor-length robes. This dancing partner has the precise footwork of someone very accustomed to stepping around magic circles without breaking them.
Sources of ‘fuel’ are another thing you might instinctively pay attention to. Fatigue-based mages might, like Pratchett’s wizards, want heavy diets to fuel regular casting. Classic D&D wizards should never pass up the opportunity to scavenge rare components, browse a market or herbalist, or gather components during a journey - and they’d likely have a practiced eye and hoarding tendencies as a result. Spirit-wranglers might consider the local spirits’ reaction to everything they do, potentially having odd habits as a result to keep everyone on side.
Wizards who have to scribe intricate diagrams probably have hobbies like knitting to improve their dexterity, the way surgeons do. Someone used to entreating spirits for aid might be really diplomatic, with a keen sense of everyone’s interests in a situation and how they can be traded off. A devil-binder might instinctively keep up a front of implacable confidence, because you have to make them think you’ve got the upper hand - or be very superstitious and over-cautious in everyday things due to the risks they constantly run.
Sorry, that got very long