perf: make initial CSS and feature application happen earlier

[txruno]

Summary

This reduces the delay between page load and ScratchTools being applied by moving style injection and feature startup earlier in the load path, while keeping the feature logic itself unchanged.

Changes

• Made CSS injection start immediately instead of waiting only for the next head mutation.
• Made style retrieval from the background script resilient during startup so it can wait for cache readiness instead of returning too early.
• Pre-warmed the cache on features changes and during tab loading to reduce first-load races.
• Kept the changes limited to the injection and startup path, with no changes to individual feature implementations.

Verification

• Checked on Windows 11 with Edge.
• Reviewed with GPT-5.3-codex.

Resolves #939