Shouldn't this be 'thought'?

No. "We had better" is equivalent to "We should" or "We must".

No. “Had better [bare infinitive verb]” is an expression that can usually be understood as “should [verb].”

No. Although, in my eyes, this is a more antiquated way of speaking English, “we had better” is another version of “we ought to” or “we should/must”

No; the writer is talking about a scenario in the present or the future

in your defence, ‘we had better’ is a really odd phrase. just replace it in your head with ‘we should’ or ‘it’s important that we’.

"We had better think very carefully" is basically a shorter way of saying "It would be better if we think carefully." In the past, people might’ve said something like "We had it better to think carefully," but over time, the phrase got simpler. Eventually, it became the more natural-sounding "We better think carefully," where even the word "had" gets dropped in casual speech. Now, it works kind of like "should" or "ought to" giving strong advice without sounding too forceful.

In this case, “had” is talking about the past, but from the perspective of you or y’all looking back on something in the future. “Had”, in this case, is referring to something you’ll have wanted to have done once you get to the point in the future where you are going to be thinking back on what you originally chose to do.

You usually see this as "You'd better think this through" or something. It's a warning of sorts to think of possible consequences that might follow a certain action

“Had better” is weird! Why on earth are we using the past tense “had” to discuss what we need to do in the future? I’ve never noticed that before. It’s idiomatic and inconsistent with the rest of the language. But yes it means should.

US: Along with what everyone else has said - in casual conversation, this becomes "We'd better" or even "We better" still meaning "should" or "ought to" or "must." (Or more precisely, it is better for us to do this thing than to not do it) Also adding a scene from a movie (["you better think"](https://www.youtube.com/watch?v=Vet6AHmq3_s)) showing the phrase used in context.

No

Think about it. I can't tell you to "thought about it". I can tell you to think about it.

Going is future. Thought is past. That's my initial take.

I didn’t even realize it but I read it as thought at first.

Thought would be past tense, so no.

We thought about what was. We think about what is