‘Oumuamua's incoming and outgoing speed is ~5AU/year. In 10,000 years that's 50,000AU, which is approximately the distance to the outer most region of the Oort Cloud: https://en.wikipedia.org/wiki/Oort_cloud

I always thought the Oort cloud was a scientifically proven thing but apparently it's "a theoretical cloud of predominantly icy planetesimals proposed to surround the Sun at distances ranging from 2,000 to 200,000 au (0.03 to 3.2 light-years)"

Thanks for correcting my similar misimpression.

It’s curious to note that the proposed outer limit of the Oort cloud (3.2 ly) is more than half the distance to the closest star system (4.4 ly) [1] though I’m unclear whether the cloud would be roughly spherical or have some sort of directionality.

[1]: https://en.wikipedia.org/wiki/Alpha_Centauri

Too faint to be proven with our current instruments.

But it would still take way less than 10000 years to cross the heliopshere boundary (it took 40 years for the Voyagers probes). It is probably referring to the gravitational sphere of influence of the solar system (marked by the Oort cloud) 1 to 2 light years away.

Could be the distance at which the sun's gravitational influence is comparable to that of the surrounding stars. This would vary over time, but as a rough estimate it's probably alright.