feat(tui): use stdout for rendering

[orhun]

Description of change

Use stdout instead of stderr, see https://blog.orhun.dev/stdout-vs-stderr/

How has this been tested? (if applicable)

Locally.

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 5 lines in your changes missing coverage. Please review.

Project coverage is 3.34%. Comparing base (ffb35ea) to head (35d710b).
Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
src/tui/mod.rs	0.00%	4 Missing ⚠️
src/lib.rs	0.00%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff            @@
##            main     #79      +/-   ##
========================================
+ Coverage   3.33%   3.34%   +0.01%     
========================================
  Files         19      19              
  Lines       2407    2401       -6     
========================================
  Hits          80      80              
+ Misses      2327    2321       -6     

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