Hm… as the て-form of だ above all, with most functions being derived from that? Or as a mix between that and a ‘means’ particle. In the case of 君は君でいいよ, I’d say either meaning works. You are good just being you, or you are good even if the basis of your lifestyle and existence is you. For その時はその時で, I guess the て-form interpretation is good if you want to focus on ‘that time being that time’ and not being presently relevant, or being different from some other time. Can we use the ‘means’ particle interpretation? Well, maybe this is technically an incorrect or imprecise interpretation, but it seems like it’s also explained by some sites as meaning ‘when that time comes’, and it certainly seems to be used that way by some people, so you could say it’s kinda like how some people explain the existence of 後で: one uses ‘that [point in] time’ to consider the issue. I think the て-form interpretation is more appropriate in this case, but I think both work.
That’s basically it. Fun fact: apparently で is actually descended from に+て in Classical Japanese, but because I haven’t had enough time to study the details of Classical Japanese grammar, I’m not sure how to interpret that, especially because に might be the particle or one of the forms of the old copula なり (basically the classical version of だ・である). I guess we can just treat that as a bit of trivia for now. Hahaha.

Not sure about that though.
