I am assuming this thread is general is to iron out some of the 'confusing' and seemingly 'illogical' quirks around the AI being annoyed during expansion phases.
Thank you for all the input, everyone, lots of good stuff here.
"Forward settling" and "settling too near the AI" are distinct from each other. The latter triggers the expansion warning, the former will trigger additional aggression for your bold move.
If an expansionist AI were to pop up and complain about the player being in the way of their forward settling, that should be its own message (the AI being an aggressive jerk, not "you're settling too near me").
Separating out the two, i would define settling too near the AI as any city which would interfere with or with a potential initial ring of cities around a capital city therefore if we took a simple straight line, any city settled within 14 tiles of a capital city.
Which i would consider their basic sphere of expected influence and is worked out as the new city tile(1) plus potential sphere of that city(3) plus forward sphere (or potential sphere) of ring city(3) plus ring city tile(1) plus rear sphere of ring city(3) plus sphere of capital(3).
If not going tradition this could possibly be reduced to 10 tiles as cities are likely to be clustered much closer to each other and borders of cities are likely to be smaller when not going tradition.
I would say any city settled more than 7 tiles away from the settlers nearest city should be classed as forward settled and come under the umbrella of 'wary of your forward settling'.
If that city is not particularly close to them but potentially prevents them from expanding or moving through the area. e.g. a city planted in a bottle-neck which prevents them from freely moving from one area to another then it should be seen more negatively (not sure how much the AI can or does calculate/plan that far forward in time).
If the city is settled with 7 tiles of one of their cities i would add on 'border tension'.
If the city actively blocks the AI's expansion plans. i.e. it prevents the AI from settling a city it planned to settle then it would come under 'settling too agressively' with an increased malice if the AI now has no where else to settle because of that city.
Looking specifically at some of the (potential) quirks.
Most malice should be calculated when that city is settled with the exception of 'border tension' which has a broader remit really. Debuffs should not occur because the AI settled a city or captured a city which brought it too close to a city you already settled.
I make an exception for 'border tension' but i would say this should only be the case if the AI still has plans to expand. I see it as illogical that the AI should settle a city near another civ and then get 'border tension' if they have no plans to expand further and instead in the case the AI wants to expand futher i would see a debuff of 'AI covets your lands' as a much better description.
If a 3rd party city is captured which brings us under this general umbrella then 'forward settling' should not be a consideration at all but this should come under potential 'border tension' and factor in relations between the two parties. If the two parties are friendly and particularly if they are both at war with the 3rd party then there should be no issue unless the AI was planning to take that city and then may feel slightly agrieved you took it first.
If your not on friendly terms then they now have a potentially agressive neighbour on their border and this would obviously come under 'border tension'