Intermission: Japanese japanese grammar is bad, too, actually
In japanese school grammar, で is considered the て "particle" of だ. (Well, they don't distinguish the て form and て particle, but same difference.) This is because of the way it can act like a conjunction. Make sure not to confuse the words "conjugation" and "conjunction".
It's confusing when you learn the etymology of だ, because you end up with a system where で and だ are derived from eachother with に caught in the crossfire.
ツインテールになりました
I became twintails.
本当にツインテールで嬉しい
(Garbled dysfluent otaku noises)
The easiest way to think of things is that they lead back to に and て, not だ. But it's important to remember that japanese school grammar still considers で to be the て "particle" of だ, because it's allowed to act like it is.
This is one of the reasons I presented the て "particle" and て "form" as different things.
Some instances of にて might actually be a fossilized proto-japanese copula, not a combination of the に and て particles, but it basically merged with the case particle sequence にて at some point, and both interpretations are valid. This "fossilized proto-japanese copula" is basically treated as the reason why で is allowed to "act like the て particle of だ" sometimes.