Assume we survive climate change as a technologically advanced society & that no other natural disaster or war wipe us out, so you really think you can predict what sort of technology will or will not be available to humans 1,000 years from now? How about 1,000,000?
If in those time spans we figure out a way to sustain 1g acceleration throughout the trip (currently not achievable but less sci-fi than FTL) we can reach nearby stars within the lifetime of the astronauts: https://www.forbes.com/sites/startswithabang/2021/12/30/how-...