Since [[ is part of the bash grammar and [ is a command built into the shell, both are documented in the bash manual itself.
[[ is documented under SHELL GRAMMAR/Compound Commands and also under CONDITIONAL EXPRESSIONS (as is [), and [ is further documented together with the test built in command under SHELL BUILTIN COMMANDS.
The test manual that you read with man test documents the external test and [ commands, probably available as /usr/bin/test and /usr/bin/[ (or possibly under /bin depending on what Unix you use).
Related: