Discontinuous effects, yes.

A stable climate functions more like a light switch than a dimmer switch. There is an "off", and once we go there getting back is really hard. It's almost like a one way switch.

As one example of a feedback loop, when polar ice melts, the area effectively turns from white (ice) to black (ocean). This area then absorbs more heat, driving more heating. So that's one feedback loop.

I think the feedback loops are kind of cool to study. Methane emissions in the tundra. Greenland melting causes more melting. Higher temps cause more water vapor that absorbs heat.

That doesn't give you specifics on where the line is. But wanted to give you an idea about the discontinuity, that there is a threshold vs dimmer switch.

P.S. I plugged your question into ChatGPT but the response was vague.

A) We've already passed the expected point of no return for 0.5 (warned about as early as the 1960s as I recall) and 1.0. As of 2023 we have already experienced years at as much as 1.2 degrees (above pre-industrial average).

B) The 1.5 degree budget, as I recall is the "best wish" case of the 2015 Paris agreement.

C) The 2 degree budget is the "worst case" allowable by the 2015 Paris agreement.

D) The Paris agreement was based on previous IPCC reports on some of the expected outcomes at 1.5 degree and 2 degree budgets. The Paris agreement was largely trying to pick the smallest number that still seemed feasible in 2015.

I think it was a compromise between achievability and limiting damage what made it to be accepted decades ago. It was unrealistic to ask to not reach 1.5ºC back then, but the increase should be as low as possible to avoid reaching tipping points and triggering positive feedback loops that could put things beyond our possibility of control.

Things are not binary, we are talking about global average temperatures, not the temperature you reach some day or season in a region. So you have to deal with uncertainty and that with higher global average temperature you will have the smaller version of the loops, even if you didn't reach the budget yet. But when you surpass enough them, then you will have more players that are changing the climate, influencing each other, and things will change faster. And there the decimal resolution may lose its meaning, your range of confidence will be much wider.