docs(mcp): clarify artifact filename resolution

[Tim Rogers (timrogers)]

Summary

• Clarify that explicit relative filename values for screenshots and videos are resolved against the directory provided by the MCP client (or the server working directory as a fallback), not the configured output directory.
• Document that omitting filename generates the default artifact name inside the configured output directory.
• Add a tool-list contract test for both filename descriptions.

Background

This distinction is surprising when the server is started with an output directory such as:

--output-dir /tmp/playwright-mcp

With that configuration, browser_start_video({ "filename": "site-interaction.webm" }) can write /tmp/site-interaction.webm when the directory provided by the MCP client is /tmp, rather than /tmp/playwright-mcp/site-interaction.webm.

Screenshots follow the same shared resolution behavior:

• browser_take_screenshot({ "filename": "named.png" }) writes the explicit relative filename under the directory provided by the client.
• browser_take_screenshot({}) writes an auto-generated page-{timestamp}.png under the configured output directory.

The existing screenshot description was particularly misleading because it recommended relative filenames "to stay within the output directory."

Validation

• Reproduced video and screenshot behavior with real MCP invocations using separate client workspace and output directories.
• Confirmed explicit relative filenames were written under the client-provided directory and omitted filenames were generated under --output-dir.
• Added and ran the focused MCP capability test that asserts both published tool descriptions.
• Ran ESLint on the modified source and test files.

Fixes #42528

[github-actions]

Test results for "MCP"

8288 passed, 1371 skipped

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Merge workflow run.