Feat: Implement password prompt as a standalone prompt

[SBoudrias]

Extracted the core rewrite from #1334 (cc @matteosacchetto).

Since this other PR is blocked on finding the right key-binding, I want to unblock other work (like the theme branch) I punted upon to not heavily conflict with the rewrite. Separating the rewrite should reduce the friction 🤞🏻

[codecov]

Codecov Report

Attention: 2 lines in your changes are missing coverage. Please review.

Comparison is base (c186dc2) 94.48% compared to head (0d9eb82) 94.48%.
Report is 1 commits behind head on master.

Files	Patch %	Lines
packages/password/src/index.mts	96.96%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1353      +/-   ##
==========================================
- Coverage   94.48%   94.48%   -0.01%     
==========================================
  Files          51       51              
  Lines        4423     4457      +34     
  Branches      772      775       +3     
==========================================
+ Hits         4179     4211      +32     
- Misses        239      241       +2     
  Partials        5        5              

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.