Use playwright install-deps to avoid fragile output parsing

[djbender]

Summary

• Replace fragile npx playwright install --dry-run output parsing with the documented playwright install-deps subcommand
• Unblocks Bump playwright from 1.59.1 to 1.60.0 #195 (Playwright 1.60.0 bump) — the 1.60.0 release reformatted dry-run output so the extracted command contains an unescaped (, causing sh: 1: Syntax error: "(" unexpected in the CI Test job

Root cause

The previous step did:

PLAYWRIGHT_INSTALL_CMD=\$(npx playwright install --dry-run --with-deps chromium | head -1 | sed ...)
sudo sh -c "\$PLAYWRIGHT_INSTALL_CMD"

This scrapes a non-contract output line. Playwright 1.60.0 changed that line so the extracted string includes characters that don't parse in plain sh. playwright install-deps is the documented CLI for "install system packages but not browsers" — exactly what this step needs, since the next step uses an actions/cache for the browser binaries.

Test plan

• CI Test job passes on this PR (was failing on Bump playwright from 1.59.1 to 1.60.0 #195 with shell syntax error)
• After merge, rebase Bump playwright from 1.59.1 to 1.60.0 #195 against main and confirm its CI goes green

[djbender]

Superseded — the same workflow fix has been pushed directly onto #195's branch so the playwright bump can land in one PR.