I think you are wrong to say there do seem to be "some things happening that might be climate change related" i.e. where you say might it should be saying certain!
I'm not sure there actually is evidence for a definite increase in the severity of many extreme events. From what I recall of the summary from IPCC AR6, there is as yet no clear signal for most such events. The IPCC suggests that for most extreme events, it is likely there have been increases in either frequency or severity, but there is no certainty as yet. The only things we know for sure are happening are more frequent and intense heat extremes.
In terms of temperature increases over time, while the physics can give us some sense of what we can expect from a doubling of CO2 there are a lot of uncertainties, for example are cloud feedbacks net negative or positive? Another interesting facet might be unexpected consequences. For example, changes to high altitude cloud responses to ship tracks in the Atlantic has contributed to a warming of the Atlantic. This is still a human-induced change, but is it directly down to CO2 emissions?
[But researchers are now waking up to another factor, one that could be filed under the category of unintended consequences: disappearing clouds known as ship tracks. Regulations imposed in 2020 by the United Nations’s International Maritime Organization (IMO) have cut ships’ sulfur pollution by more than 80% and improved air quality worldwide. The reduction has also lessened the effect of sulfate particles in seeding and brightening the distinctive low-lying, reflective clouds that follow in the wake of ships and help cool the planet. The 2020 IMO rule “is a big natural experiment,” says Duncan Watson-Parris, an atmospheric physicist at the Scripps Institution of Oceanography. “We’re changing the clouds.”]
Overall, the IPCC finds that the long term atmospheric response should be in the range 2C to 5C for a doubling of CO2 with the central estimate around 3C. The short term response (this century) is from about 1C to 2.5C with the central estimate about 1.8C. That's for a doubling of CO2, the question might be, will that happen. At curent rates we will see that happen in around 80 years, but CO2 rates of increase have been falling since about 2015. It's debateable, given that we are rapidly depleting oil and coal reserves while also increasing use of renewables, whether we will actually reach 560ppm by 2100.
I think we are seeing about 1.2C of increase for the global average temperature as at today, so it seems possible that we will not exceed 2.00C this century. I'm not convinced 2C will result in catastrophe.
Now, I wouldn't say I have great insight into climate change, but I *have* been following tihe science pretty closely for around a decade. I do believe that the globe must warm from rising emissions, I am just not so certain it is as bad as people are making out. Time will tell, I guess.