msg: make --msg-level affect --log-file too

But --msg-level can only raise the log level used for --log-file,
because the original idea with --log-file was that it'd log verbose
messages to disk even if terminal logging is lower than -v or fully
disabled.

DOCS/man/options.rst

@@ -403,8 +403,9 @@ Program Behavior
 
 ``--log-file=<path>``
     Opens the given path for writing, and print log messages to it. Existing
-    files will be truncated. The log level always corresponds to ``-v``,
-    regardless of terminal verbosity levels.
+    files will be truncated. The log level is at least ``-v``, but can be
+    raised via ``--msg-level`` (the option cannot lower it below the forced
+    minimum log level).
 
 ``--config-dir=<path>``
     Force a different configuration directory. If this is set, the given
@@ -3380,6 +3381,8 @@ Terminal
     can use the module names printed in the output (prefixed to each line in
     ``[...]``) to limit the output to interesting modules.
 
+    This also affects ``--log-file``, and in certain cases libmpv API logging.
+
     .. note::
 
         Some messages are printed before the command line is parsed and are

common/msg.c

@@ -285,7 +285,7 @@ static void write_log_file(struct mp_log *log, int lev, char *text)
 {
     struct mp_log_root *root = log->root;
 
-    if (lev > MSGL_V || !root->log_file)
+    if (!root->log_file || lev > MPMAX(MSGL_V, log->terminal_level))
         return;
 
     fprintf(root->log_file, "[%8.3f][%c][%s] %s",