Why do some functions only work in the first column?

That's not how you use VLOOKUP, and you don't need VLOOKUP.

VLOOKUP(search-for, columns-range, return-column, close-match)

The search-for parameter and columns-range parameter are correct for how you are using it but the "return-column" needs to always be 1 because columns-range only has one column. When you use COLUMN(cell) as that number, it is 1 in column A but not in any other column. Regardless, there is no need to use VLOOKUP when you already have the value you are looking for (i.e., the search-for parameter) which you got by using the SMALL function.

With "Entries" being column B,

=IFERROR(SMALL(B, ROW()-1),"")

The blue triangles are from including empty rows in the SMALL function. One way to get around that is

=IFERROR(SMALL(OFFSET(B$1,1,0,COUNT(B),1),ROW()−1),"")

The blue warning triangles are just annoying to look at. They cause no problems. You can get rid of them by not having extra (blank) rows in 'Entries Table' or by limiting the range to only the populated rows. You are right to be concerned about using OFFSET in thousands of rows of formulas. It is supposedly a slow function. It might not matter but it is a consideration as the row count grows.

VLOOKUP can be used to return the value from column C but XLOOKUP is newer and better. There may be some cases where VLOOKUP is better but this isn't one of them.

Formula in column C of Sorted Table would be

=XLOOKUP(B,Entries Table::B,Entries Table::C,"not found",0)