Sadly in this year of 2023 it's clear that no, we're running headlong into it. Personally though I suspect there is no one filter, just a series of them.
Nuclear weapons are a filter.
Climate change is a filter.
Future biotech is a filter.
Probably future nanotech is a filter.
There's always going to be some new tech we create long before our human nature has adapted us to its responsible use, and each one carries a risk of setting our civilization back so far it never recovers. That's the filter, the nature of organisms which reach the point we do is the filter itself.
I agree. My theory is the great filter is most definitely in front of us. I think intelligence will move through the next filter, however, I highly doubt human beings will make it through.
These discussions invariably miss the obvious filter which is "interstellar travel is hard".
The most plausible scenario for interstellar travel requires deuterium-deuterium fusion and the ability to "live off the land" between the stars. Note a Pluto-sized "planet" could be disassembled and consumed entirely to construct a habitat with more square footage than the Earth. Rouge planets like that might be really common, certainly most of the usable mass in the galaxy is in Oort cloud objects.
If it takes 10,000 years to cross to another planetary system but travelers can stop anywhere between and colonize, travelers might have no interest at all in bone-dry inner solar system bodies. After 10,000 years in interstellar space such travelers would be highly unlikely to have a "space shuttle" for landing on an Earth like planet, with some luck they would have plans for their 3-d printer but they very well might have optimized their printers for the stuff they actually make and the old plans for chemical rocket engines, heat shields and such might not work the first time. Development of such a "space shuttle" might take as long for them as it did for us, if only because they won't have a whole civilization available.
The evidence that they haven't been here is that we have Ceres and Pluto and they haven't been turned into small ringworlds or other habitats.
If it really is a 10,000-year trip then you are left with the motivation people have to do it, particularly if you consider the Von Newman machine scenarios where quite likely your ancestors won't be around or won't remember when they machine finally returns results. There's always the outside risk that somebody will track the machines back to their source and decide to bomb us with a scaled-up "Breakthrough Starshot" as in the book The Killing Star. People are indifferent to make sacrifices to avert catastrophe in the next 100 years, how do you expect them to care about something more distant.
With all the stars and planets out there I wouldn't be surprised if something had made the trip from one star to the next, but it's not sufficient to do that once, colonization requires doing that over and over again and I think the odds are long for that and any life that manages the feat may well be transformed considerably by it.
(e.g. if we were "serious" about colonizing the galaxy note that most of the habitable places as defined by having liquid water are underneath the ice in an outer solar system body somewhere. Creatures who were serious about this might alter their bodies and metabolism so they can survive in the places that are actually available, for one thing...)
Sadly in this year of 2023 it's clear that no, we're running headlong into it. Personally though I suspect there is no one filter, just a series of them.
Nuclear weapons are a filter.
Climate change is a filter.
Future biotech is a filter.
Probably future nanotech is a filter.
There's always going to be some new tech we create long before our human nature has adapted us to its responsible use, and each one carries a risk of setting our civilization back so far it never recovers. That's the filter, the nature of organisms which reach the point we do is the filter itself.