fix: Seerr login browser cookie handling on container deployment

[v3DJG6GL]

Pull Request Description

• Seerr connection fails on container deploymenth with No session cookie returned by server.

• Browsers process the set-cookie response header internally but never expose it to JavaScript. Fladder can't capture the session cookie and treats login as failed. Much better described by @Wunderharke: Jellyseerr local login fails from web (proxmox helper script); works fine from android #710 (comment)

• This fix uses a conditional-import BrowserClient with withCredentials: true so the browser manages session cookies on its own. Since Fladder can't see whether a cookie was set, a __browser_managed__ sentinel is stored on web instead,
  and _authHeaders skips the manual Cookie header since the browser should already attach it.

• This feature was part of PR feat: Seerr QC login, password-login hide, auto-URL scheme, new ENV vars | fix: Set-Cookie #812

NOTE: Cross-origin setups still require CORS headers on the Seerr side

Testing Build

ghcr.io/v3djg6gl/fladder:test-seerr-web-login-fix

Issue Being Fixed

• Jellyseerr local login fails from web (proxmox helper script); works fine from android #710 (comment)

Screenshots / Recordings

N/A

Notes

AI Disclosure

Developed with assistance from Claude Code (Opus 4.6). The AI helped me identify the related files, code parts and proposed possible code modifications and fixes.
I've manually reviewed, cleaned, refactored and hardened the code the best I could, but since my Dart capabilities are not that good, I see this PR more as a proposal/idea.
A Proper code review is required in any case...

Checklist

• If a new package was added, did you ensure it works for all supported platforms? Is the package well maintained
• Check that any changes are related to the issue at hand.

[PartyDonut]

LGTM, Thanks.