You're still doing it. When you say "We're still competing with other species, and we're still vulnerable to things like the effects of climate change, so if we completely stop evolving", what you imply is that if we keep evolving, we will improve until we can survive climate change and outcompete other species.

Again, that's not how it works - dinosaurs didn't evolve to be meteor resistant, and carrying on evolving could as well lead to our extinction as to our saving, or indeed to our losing intelligence and becoming a niche species again.

And that's aside from the fact that even with technological immortality, we'd still have people dieing and being created, and evolution will still be happening - it can't not-happen.