Regarding the chagim (festivals), we know that a chag is really one day (not including the rabbinic chag a/k/a yom tov sheini). However, for Rosh hashana, Israelis observe a two day festival. So is the reason Israelis observe two days of Rosh hashana because they believe both are a biblical chag? It makes a difference whether the second day of Rosh hashana is biblical or rabbinic. It would make a difference in burying a dead body, because כבד המת takes precedence over yom tov sheini. So can a person be buried on second day Rosh hashana?
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The reason that we keep 2 days on all festivals outside of Israel is because originally it was a doubt whether the new month had been declared, and word did not reach far enough for them to know by the middle of the month. Even once the calendar was set, they maintained the minhag of their predecessors (Beitza 4b).
The Ba'al HaMe'or to Beitza 5a explains that regarding Rosh Hashana, everywhere outside the immediate Temple vicinity is like "Bavel" i.e. outside of Eretz Yisroel, because only in the Temple vicinity did they not have the doubt of if today was Yom Tov or not. So they have the "Minhag avoseihem" that we have outside of Israel by all other holidays even in Israel regarding Rosh Hashana.
Regarding burying a dead body, Rosh Hashana is actually more strict than other festivals according to some opinions in the Talmud, but nothing to do with being biblical or rabbinic - it is because of the nature of the doubt. However, the gemara is explicit that even on Rosh Hashana they allowed burying someone on the second day (Beitza 6a).
As an aside, it was a major machlokes Rishonim if Rosh Hashana should be 2 days in Israel.