That "old" Internet is still here, alive and kicking, just evolved. It's easier to follow people's blogs and websites thanks to ubiquitous RSS (even YouTube continues to support it). It tends to be more accessible, because we collectively got better at design than what we've witnessed in the GeoCities-era.
Discovery is comparatively harder - search has been dominated by noise. Word of mouth still works however, and is better than before - there are more people actively engaged in curating catalogues, like "awesome X" or <https://kagi.com/smallweb/>.
Most of it is also at little risk of being "eaten", because the infrastructure on which it is built is still a lot like the "old" Internet - very few single points of failure[1]. Even Kagi's "Small Web" is a Github repository (and being such, you can easily mirror it).
[1]: Two such PoFs are DNS, and cloudflarization (no thanks to the aggressive bots). Unfortunately, CloudFlare also requires you to host your DNS there, so switching away is double-tricky.