1. PostgreSQL 13 Official Documentation, psql Meta-Commands: The \connect or \c command is documented as the method to establish a new connection to a PostgreSQL server. The documentation states, "If the new connection is successfully made, the previous connection is closed."
Source: PostgreSQL 13 Documentation, Chapter 53. psql, Section 53.3. Meta-Commands.
2. PostgreSQL 13 Official Documentation, SQL Commands: The official list of SQL commands for PostgreSQL 13 does not include USE or SWITCH as commands for changing the database context.
Source: PostgreSQL 13 Documentation, Part VI. Reference, SQL Commands.
3. PostgreSQL 13 Official Documentation, SET Command: The documentation for the SET command confirms its purpose is to change session-level run-time parameters, such as SET searchpath TO myschema;, not to switch the database connection.
Source: PostgreSQL 13 Documentation, SQL Commands, SET.