Those first two are entirely invalid in T-SQL. Even attempting to write it as SELECT IIF(NULL AND 1=1, 1, 0) doesn't work. The AND operation can only be applied to a boolean type and the only way to get that is as the result of a comparison and it can't be stored or passed anywhere.
Also the UNIQUE constraint does not allow insert of a second NULL. I tried that both using the constraint syntax and by creating a unique index.
In Postgres you can chose whether to treat NULLs as distinct or not (meaning that when treating NULLs as NOT DISTINCT you can insert many for an otherwise unique row).
Those first two are entirely invalid in T-SQL. Even attempting to write it as SELECT IIF(NULL AND 1=1, 1, 0) doesn't work. The AND operation can only be applied to a boolean type and the only way to get that is as the result of a comparison and it can't be stored or passed anywhere.
Also the UNIQUE constraint does not allow insert of a second NULL. I tried that both using the constraint syntax and by creating a unique index.