This is wrong. There is no holiday called "Passover" in the Tanach. Holidays are not given proper names, they're called by events relevant to the holiday. The Feast of Unleavened Bread is also called the Feast of the Passover, because it's the holiday that the Passover sacrifice was eaten on. The Feast of Unleavened Bread aka the Feast of Passover begins on Nisan the 15th at night and continues for 7 days. It's not a 24 hour period, it's another name for the same holiday. The day prior to the Feast, the 14th, is not a holiday, it's simply the day on which one removes all unleavened bread in order to sacrifice the Passover offering (which can't be sacrificed with unleavened bread around). There are no special observances on the 14th, because again, although the Passover sacrifice is being sacrificed on this day, it's not eaten until the night time. The offering must be eaten on the night of the 15th and can't be eaten after dawn, so there's a practical reason why we don't wait until the night to start the sacrifices. So the only time the word "Passover" refers to a holiday, is when the word "festival" is attached to it. Otherwise it refers to the actual sacrifice. The proper noun "Passover" for the holiday is a much later name for the holiday, similar to how Rosh HaShanah is a later name for the Day of Trumpets.
The reason why those of us in the diaspora add an extra day (technically two extra days on Passover and Tabernacles) was because the amount of days in a month used to be subject to change and the Sanhedrin was worried that messengers wouldn't make it to all the countries in time to let them know. The extra day covers the possible change to the calendar. Today, that is no the reason as we have a fixed calendar. The reason we do so today is because this is the custom we inherited from our fathers and in case a problem ever crops up again.
The Orthodox Jews I used to work told me that the first 24-hour period from the beginning of Nisan 15 at sunset is special in that it is the time within which a Seder is observed and no work is performed regardless of whether one is in Israel or not. Some of them would be willing to work on the second day. Not Lubavitchers though. And not those who planned a large second Seder. Anyway, they would all use Passover in the two senses I mentioned depending on context. I happened to notice that in Israel, the word Pesach alone without qualifiers is the one-day legal holiday. Passover properly is as you say the entire 7/8 day period. I was just mentioning that the intended meaning may vary depending on who is saying it in what context.
You said that unless the word ‘festival’ was used, the word refers to the sacrifice. This raises questions when the Greek of Mark is examined.
Mark 14:1 En de to pascha kai ta azuma meta duo hēmeras
Literally: ‘It was yet the passover and the unleavened after two days’.
KJV: After two days was [the feast of] the passover, and of unleavened bread
Mark links the word Passover and the Feast of the Unleavened Bread here, which would make ‘Passover’ mean the festival. But in that case, why say the Passover and the feast?
Mark 14:12 kai iē prōtē hēmera tōn azumōn ho te pascha ethuon
Literally: ‘and to the before-most day of-the unleavened when the passover they-sacrificed’
KJV: And the first day of unleavened bread, when they killed the Passover
Here the word ‘passover’ is used in reference to the sacrifice, which would be the afternoon of 14 Nisan. Yet it is also called the first day of unleavened bread, which properly did not begin until sunset, the beginning of Nisan 15.
I agree with you that this does not make strict sense. As I have written earlier, Mark’s narrative connects Jesus to the sacrifice in an indirect manner. Is this just another example of that?
The problem with starting months with the confirmed sighting of the new moon was that the lunar cycle is twenty-nine and a half days long. That means two possible days only one of which is right. Thanks to Hillel II (according to tradition) the mathematically based rabbinic calendar settles the matter regardless of sighting.