Please note the Court temporarily upheld the 5th Circuit’s temporary ruling. Oral Argument takes place on April 5th in the 5th Circuit re the underlying constitutional issue whether Texas can do their own thing re federal immigration laws and enforcement.
Justice Barrett’s opinion and the dissenting opinions are informative.
The Biden Administration obviously contests Texas’ assertions of power in this appeal.
As to your query, the Biden Administration does not believe the Executive Branch has unfettered authority, which is one of the reasons why Biden urged Congress to pass the bill authored by Senator Langford..
Link: https://www.supremecourt.gov/opinions/23pdf/23a814_febh.pdf