the sun - How often do stars pass close (~1ly) to the Sun?

I was curious about the same things. I believe it was in the astronomy I was referred to an online data base that gives position and velocity vectors for neighboring stars. From those I put together a spreadsheet. Here's a screen capture:

I only entered 48 of the closest stars so it's by no mean an exhaustive list.

It looks like your graphic matches my estimates which is reassuring. I don't know why the Ross Stars aren't in my list, possibly the omission is an error on my part when I was entering data to the spreadsheet.

Looks like the closest approaches are around 3 lightyears.

If each star has an Oort cloud, I believe the comets' velocity with regard to our sun would be pretty close to the star's relative velocity. Slowest star wrt our solar system seems to be Gliese 729 which is moving ~14 km/s wrt the sun.

If, for example, some of Van Maanen's Oort cloud came within a light year of our sun, they would have been moving 270 km/s. Those snowballs would have zoomed in and out of our neighborhood.

With these distances and relative velocities I don't see much opportunity for swapping comets.

It's speculated that our sun swapped comets with neighboring stars when our solar system was being formed. From Wikipedia:

Recent research has been cited by NASA hypothesizing that a large
number of Oort cloud objects are the product of an exchange of
materials between the Sun and its sibling stars as they formed and
drifted apart, and it is suggested that many—possibly the majority—of
Oort cloud objects were not formed in close proximity to the Sun.