fix: keep a running output's claim when start() is called again

The previous commit stopped the failure path from releasing a claim while the
muxer was still writing, but the resolve path could still move it. A duplicate
start() runs the whole Start() handler first: the timestamp has advanced, so
FindBestFilename resolves a different name and reassigned claimedFilePath to it.
obs_output_start() then refuses because the output is active, leaving the muxer
on its original file with nothing claiming it -- and an output with overwrite set
skips the on-disk check that would otherwise have covered it.

Only take the claim when the output is not already active. obs_output_active()
is null-safe, so an output that has not been created yet claims normally.

Rejecting the duplicate start outright would be the more thorough fix, but that
changes what the Start IPC call returns for a case Desktop can reach through
validateOrCreateOutputInstance, so it wants deciding on its own terms.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

Author: summeroff

obs-studio-server/source/osn-file-output.cpp

@@ -107,7 +107,10 @@ void osn::IFileOutput::FindBestFilename(std::string &strPath, bool noSpace, File
 
 	strPath = candidate;
 
-	if (owner)
+	// Never move the claim of an output that is already running. A duplicate start() resolves a
+	// fresh name -- the timestamp has moved on -- but obs_output_start() then refuses and the muxer
+	// stays on its original file. Reassigning here would unclaim the file actually being written.
+	if (owner && !obs_output_active(owner->GetOutput()))
 		owner->claimedFilePath = strPath;
 }