Effectively by working to conquer cancers and age related diseases/decline, and the general effort to “extend our lives”… we are making space slightly smaller for our future selves once our propulsion technology advances to the point we can achieve decent percentages of the speed of light… which there are no real technical barriers against. From solar sails to muon fusion to all sorts of other interesting technology we have yet to develop, we may not be able to break a warp barrier and go faster than light… but if we live longer, say 10 times longer, the. Suddenly 5 years shipboard time travelling to another star system doesn’t seem so bad. 5 years in a millennium of years is equivalent to a 6 month journey for someone who will live to 100.
The earth is ~4.5 billion years old. So we can say with certainty that it's possible (not guaranteed) to become a space faring race (although not a galaxy crossing one) in 4.54 billion years. If we tack the amount of time it takes to cross the whole galaxy end to end we get 4.55 billion years. The milky way galaxy is 13.61 billion years old. That means the galaxy had 9.06 billion years worth of chances to churn out a another planet that could have expanded across the galaxy from edge to edge and been here waiting when humans arrived on the scene. Planets with Earth like conditions are certainly rare but my, admittedly limited, understanding is that they're not "1 in 9.06 billion years" rare.
There are obviously other constraints here. I think your second point about wealthy technological races potentially stabilizing at zero population growth is totally reasonable. But I think the fact that space's apparent scale doesn't actually matter is the whole reason the Fermi Paradox was such an "ah-ha!" moment for many people. The reason it's a paradox is that, given all of our assumptions for variable values in the Drake Equation at the time, it really seemed like we should have met some aliens. The point was that if distance wasn't the hurdle we thought it was in the equation as currently defined, then we were either missing some relevant variables, or we had made some bad assumptions for the ones we had.
It doesn't have to, in fact (relatively) endless population growth is the prime force to push even lazy non-curious fearful aliens out of their planet and sun. That and obvious unavoidable necessity of every sun eventually becoming killer of its own ecosystem, even if their planet would be super duper stable with all meteorites under total control.
The rest I agree with, even civilization having mere 100 million years of advantage on us would be able to properly colonize non-trivial part of milky way by now, we just have to abandon star trek/wars expectations of instant communication and travel which is fine. We humans are generally pretty bad at grasping true meaning of numbers when it comes to ie astronomy.
Indeed, if human society is a guide, a society that develops interstellar travel would have to have reached a stable situation, so stable I'm not sure if massive expansion would seem desirable.
Human have no way to survive that time period, no way to create a self contained environment that would survive that time period and no civilization that's lasted a fraction of that time. The increase of human technology hasn't correlated with stability so increases in our technology don't seem like arguments for our ability to act in a long and large scale, despite being implicitly taken as such by a lot of people.
Sure, in the geological time humans study ten million years isn't much but the claim that a living creature could act in the time period is purely speculative. Speculation is fine but the rhetoric of the "Fermi Paradox" is "why don't I see of things I have only wildly speculated about, there's something weird here", which is kind of problematic.
There are other factors that are more likely to explain why we are apparently alone: civilizations might not last long enough that they would encounter us before dying out, or that they have not yet emerged. IOW we might be alone in time more than we are alone in space.
You're posing these things as though they're axiomatic for all beings; as if these beings (which don't exist) would operate exactly as we do and not have their own cultures and ways of being distinct from our own here (of which are vastly different amongst people of other countries on Earth). It's a very narrow, human-centric view.
There are also unstated economic assumptions that don't make a lot of sense. Why would they leave their planet anyway? A civilization wealthy and advanced enough to consider traveling to other planets probably does not have a population big enough to support the kind of large scale emigration needed to set up big colonies. Wealthy societies have fewer children. Then of course there is the question of why would you ever leave a planet with such advanced technology and apparent wealth? I would much rather live in any city on earth than a colony on the moon or Mars. How long would it take for those colonies to be as attractive a living space as the place we have right now?