I don't have a source to prove this but I would say the two aren't related, except in the obvious way that they both use a form of the word "good" in a way that makes sense given the meaning of that word.
The text is best interpreted by reference to the classical era
"Best" here does define "interpreted" and I would say if you had to look for an alternate form that means the same thing (and that this one might derive from), it would be "The best way of interpreting this text is by reference to the classical era". It might simply be a form of a general "adverb - verb in past participle" form, like "this was nicely done".
We had better interpret the text by reference to the classical era
The reason I wouldn't say this is a version of the previous sentence is that it sounds like you're trying to rephrase it in an active form with "We" as subject instead of "The text", and you found yourself using "had better" which is similar to "best" so you thought the two might be linked in this transformation. I would argue that this isn't the case, and that there isn't a single obvious way of re-writing the above sentence in active form, and that different ways won't match up the same. For example if I had to convert the first sentence to an active form I think my first thought would have been:
We would do best to interpret the text by reference to the classical era
Where I think "best" actually might match up in the way you suggest. Not sure though.
But at the end of the day, the transformation you did was from "This is the superior option" to -> "We should pick the superior option", and "had better" is one possible way of expressing the idea of "should". But you could have said:
We ought to interpret the text by reference to the classical era
and I think the relationship between the two sentences, how similar and different their meanings were, would have been roughly the same as in the example that uses "had better".
I won't go into the specific differences in what the sentences mean because I think Amit Mittal's answer does that fine.