What's going on with people sharing ancient CO₂ charts to argue about climate change on X?

I keep seeing posts where people share charts showing CO₂ levels over millions of years - like the Cenozoic era going back 60 million years - and using them to either prove climate change is an emergency or prove it's overblown.

One side says "look, CO₂ is doing something unprecedented" and the other side says "look, CO₂ was way higher millions of years ago and life was fine."

A few things I'm confused about:

1. The chart only covers 60 million years but Earth is 4.5 billion years old. Why is this specific window always the one people use? Is it just the best data we have or is it a framing choice?

2. People keep calling these "data" but someone pointed out it's actually proxy reconstructions from ice cores, sediment, stomatal indices etc - not direct measurements. How reliable are these reconstructions actually and has anyone independently replicated them?

3. There seems to be a debate about whether the "rate of change" matters more than the absolute level. Both sides seem pretty confident but they're talking past each other. What's the actual scientific consensus here and how much of it is genuinely settled vs still debated?

4. Is there a replication problem in climate science similar to what happened in psychology and medical research? I've seen people on both sides accuse the other of being funded to reach certain conclusions.

Not looking for political takes, just trying to understand what's actually well-established vs what's interpretive.