pushState then data-sveltekit-replacestate breaks the back button

Describe the bug

I have a modal which has links towards other pages.

---

// first-page/+page.svelte

<script>
	import { pushState } from "$app/navigation";
	import { page } from "$app/state";
	function showPopup() {
		pushState("", { showPopup: true });
	}
</script>

<button onclick={showPopup}>show popup</button>

{#if page.state.showPopup}
	<a href="/second-page">go to second page</a>
{/if}

This works fine, I correctly land in /second-page. When I go back with my browser's back button, I'm correctly redirected to /first-page, but the popup is still open while I need it to be closed.

---

I thought data-sveltekit-replacestate would solve my issue:

<a data-sveltekit-replacestate href="/second-page">go to second page</a>

But once on /second-page, after going back, the URL change to /first-page but the page doesn't load: the content of /second-page is still shown.

---

data-sveltekit-reload works as expected but the UX isn't great.

---

Is this behaviour expected? If so, is this shallow navigation actually doable without a full page reload?

Reproduction

See https://stackblitz.com/edit/sveltejs-kit-template-default-6v3iubbw?file=src%2Froutes%2F%2Bpage.svelte

Logs

System Info

System:
    OS: macOS 15.5
    CPU: (10) arm64 Apple M4
    Memory: 89.84 MB / 16.00 GB
    Shell: 5.9 - /bin/zsh
  Binaries:
    Node: 24.4.0 - /opt/homebrew/bin/node
    pnpm: 10.13.1 - /opt/homebrew/bin/pnpm
  Browsers:
    Chrome: 138.0.7204.184
  npmPackages:
    @sveltejs/adapter-auto: ^6.0.0 => 6.0.1 
    @sveltejs/adapter-static: ^3.0.8 => 3.0.8 
    @sveltejs/kit: ^2.16.0 => 2.26.1 
    @sveltejs/vite-plugin-svelte: ^6.0.0 => 6.1.0 
    svelte: ^5.25.0 => 5.37.0 
    vite: ^7.0.0 => 7.0.6

Severity

annoyance

Additional Information

No response

Start with the linked StackBlitz reproduction and reproduce the sequence using pushState, the second-page link, data-sveltekit-replacestate, and the browser back button. Trace the SvelteKit navigation and history behavior involved; done means back navigation restores /first-page with the popup closed and renders the correct page without requiring a full reload.