This is a difficult question to answer. The historicity of the Exodus, at least as described in the bible, is unlikely. See this section of the FAQ.

The earliest sources on Passover are in the bible. On numerous occasions the text describes Passover celebration in brief or more comprehensively. The most extensive description is probably Exodus 12. But its presence in multiple sources of the Torah's text would indicate that its celebration had its roots in multiple religious traditions, making it rather old, depending on what bible-dating scheme you prefer, and which source contributes which bits of the bible, both of which can be contentious and interrelated issues.

However, 2 Kings 23 references Josiah restoring Passover. This is a somewhat challenging description, since it would indicate that celebration of Passover was not known commonly at the time, and was only a celebration of the distant past. The language of the text may suggest a particular Passover observance being restored, but exactly what Josiah's reform is intended to convey is a difficult question, as is dating this text (which really goes for any part of the bible). The bible also mentions Hezekiah celebrating Passover, and he's about a century earlier.

If we take the narrative of Josiah's reform's dating at face value, and assume that it was an entirely new era in Passover celebration (even if it was restoration of an earlier practice, presumably it would've been different, and perhaps it was a new innovation), Passover's celebration began in 622 BCE, so this spring would've been the 2636th Passover continuously celebrated. But I'd be very hesitant to give that number without a lot of qualification. Based on that, my conservative answer would be "at least 2500 years". But since Passover may've developed from earlier origins, defining when Passover begins even if we had a completely reliable comprehensive history of the holiday would not be trivial.

Do we know how the holiday's recognition has changed over time?

To an extent. First, over time the focus switched from the temple sacrifices to the pascal offering itself. Then, after the destruction of the Temple, the focus shifts again to the retelling of the Passover story, which is mentioned in the bible but plays second fiddle to the other paschal activities. And there are innumerable smaller ways in which observance has shifted, from change in what plant was the bitter herb to tweaks to the liturgy.

Sources:

Chavel, Simeon. "The Second passover, pilgrimage, and the Centralized Cult." Harvard Theological Review 102.1 (2009): 1-24.

Niesiołowski-Spanò, Łukasz. "Passover, the Jewish cultic calendar and the Torah." Palamedes: A Journal of Ancient History 2 (2007): 35-54.