I would say the bust had no substantial impact on technology side of thing. Perhaps the pricing became bit more modest, and sure, lots of careers were "filtered out".
I think that it did, because it focused development efforts of companies that remained in business. Many failed dot-coms should have failed before the bust, but they kept acting like working businesses as long as they had capital available. They diluted markets, absorbed development talent by offering equity and large salaries, and in general distorted the whole industry.
After the bust, the technologies and idea that got attention/effort/built up were the ones with a solid foundation, not the pipe dreams.
It was a Microsoft-only thing for a while though, until Mozilla/Safari/Opera implemented their own versions. That took a few years IIRC.
At any rate, Gmail was what made the world really take notice of what AJAX could do.
The stuff built in the early dot-com era was typically garbage from a technical standpoint. Heaps and heaps and heaps of spaghetti code written in PHP, Perl, and ASP Classic. You could theoretically write maintainable code in those technologies if you were truly dedicated but this was decidedly not the norm.
Think of literally any basic best practice for writing either the server or client portions of a web application that we might follow in 2019. In, say, 1997 those best practices hadn't been invented yet and even if you traveled back to 1997 in a time machine you couldn't implement some of them since the technology hadn't been invented yet.
From a technical perspective, roughly 2002-2006 was when things started to get really good from a technical standpoint.
- A lot of untalented folks (people calling themselves "developers" but with no real coding ability) were filtered out of the industry.
- A lot of lessons had been learned about how to build this stuff.
- More and more people were getting high-speed internet access.
- The use of AJAX to build responsive client-side applications became a thing, thanks largely to...
- ...Google, who released two absolutely world-shaking web applications in Gmail and Google Maps. These became something of a guiding light in a number of ways. Both from a technical showcase of what could be accomplished with web standards, and a design perspective... it showed a lot of pointy-haired bosses that what people wanted was minimal design and maximum usefulness, not a flashy multimedia experience.
- Other "Web 2.0" tech like RSS matured and enabled LOTS of cool demos (sadly we've moved away from this...)
- Pressure from Firefox forced Microsoft to finally embrace some more web standards and we edged away from the brink of a Microsoft-ruled internet