[Bug report] routePath watcher different behavior in e2e and downstream

[Mister-Hope]

Description

For core e2e, watchers are called expected:

Reproduction:

1. checkout to render-debug branch
2. built the project with pnpm build
3. run e2e docs with cd e2e && pnpm docs:dev (build is same)

---

But for downstream repos (tested on theme-hope and ecosystem, the watchers are not called in the same sequence:

Reproduction:

1. checkout to render-debug branch in ecosystem
2. built the project with pnpm build
3. run docs with cd docs && pnpm docs:dev (build is same)

This means any downstream plugins or theme can not read the page content DOM properly after navigating. For all the time, we are introducing a delay option for this.

Reproduction

See main text

Used Package Manager

pnpm

System Info

Not needed

[github-actions]

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