I tend to agree with Therese that Emma was heiress of 30,000 rather than already in possession of it, since her father was still alive, and Regency society was a patriarchal society. If Emma had inherited money elsewhere and was richer than her elder sister, this would be unusual, so if JA intended it that way, I think it would have been specifically mentioned, to describe her unusual situation. But instead, we're told that Emma's distinction from Isabella is that she was much cleverer as a child than her older sister, not that she had somehow inherited some more money.

A fortune of 60,000 pounds plus a small to moderate estate like Hartfield would already make the Woodhouses rich by JA standards. It could bring in an income of perhaps 4,000 a year, and in S&S, Col Brandon, with 2,000 a year is described as rich, and in P&P, Bingley with 4,000 to 5,000 a year is certainly rich. I think the Longbourn estate of 2,000 a year in P&P is bigger than the Hartfield estate -- Longbourn has the village of Longbourn, whereas there is no village of Hartfield, it was only adjoined to the village of Highbury -- but the Bennets had hardly any money from other sources. The Woodhouses had a large house on their small estate because of their money from other sources.