We're not getting to a planet 100 light years away with chemical rockets so presumably the future inhabitants will be able to use high efficiency rockets to leave it.

I don’t think interstellar travel necessarily implies much better tech than we currently have. I mean, Project Orion style nuke-powered spaceships can get you there in a lifetime but unless you wanna nuke your colony whenever someone needs to leave you still might be stuck on the surface.

What? A nuke in space will have very little impact on a planet. A nuke on a planet doesn't have much impact on the planet either: see all the tests done on earth.

It's a non-trivial number of nukes on every single launch. If it becomes popular, it will have a very noticeable effect on a planet.

Nuclear propulsion isn't the only alternative we have for reaching low orbits. Land-powered rockets are probably much better, and there is always the odd high-elevation rail or space elevator (but those get bad fast on large planets).

There are non-rocket ways to space, like a catapult or maglev accelerator. Or ways to assist the rocket outside the rocket equation, like a spaceplane launch platform. Or even Project Orion nuclear explosion propulsion. (Which is subject to the rocket equation, but with nuclear rather than chemical fuel for a much higher multiplier of energy per mass.)

I'm skeptical a catapult could ever work in an atmosphere as thick as Earth's. The drag would be incredible.

It'd just be 13 km/s to low orbit (or 19 km/s to escape), which isn't really that much for small payloads -- New Horizons had a total of 17 km/s delta-v. You don't even need to look at space elevators or fission or fusion launch systems, all of which are probably viable on first principles.

That orbit or escape velocity really is that much. The rocket equation is exponential, such that even a small change in the required speed means a large change in requirements. The difference between Earth's escape velocity of 11 km/s and this planet's of 19 is actually quite huge. Imagine you build an 11 km/s rocket as you would on Earth... to get it off this other planet, first you have to accelerate that rocket and all its fuel to 8 km/s.

The rocket equation is Δv = Ve ln (m0 / m1), where Ve is exhaust velocity, m0 is payload mass, m1 is mass including fuel. To get 19/11 as much Δv, you need a fuel/mass ratio of e^(19/11) = 5.6 times greater.