S.386 was introduced in the Senate by Mike Lee in 2019 [1]
There was a unanimous consent on it in 2021 [2] but the bill expired (?) because Dick Durbin, senator from IL wont table it (I dont clearly understand the process in the Senate but some people who follow this had expressed anger at Durbin for not doing anything - https://www.durbinisracist.com/)
It was reintroduced in Congress as Eagle Act [3] but its been stalled ever since. It ironic that people think Democrats want open borders while the same Democrats could not even pass a sane bill for legal immigration (especially for immigrants who contribute a whole lot to the US) with their majorities while immigration was a top agenda for President Biden. Not to mention all the big tech companies with big lobbies cant get this move at all.
[1] https://www.congress.gov/bill/116th-congress/senate-bill/386... [2] https://cis.org/Vaughan/Senate-S386-HR1044-Country-Cap [3] https://eagleact.info