Coder Tasks presets not set correctly when switching between templates #20465

Description

When switching between templates with presets in the Coder Tasks UI, the presets don't get populated correctly. The presets sometimes don't show up, but when switching back and forth they may intermittently appear.

Reproduction

1. Have at least two templates with presets configured
2. Navigate to Coder Tasks UI and switch between templates
3. Observe that presets don't consistently populate when switching

Additional Context

• Originally reported on v2.26.1-devel+65335bc7d (on ai.coder.com)
• Cian reproduced similar behavior on v2.27.1-devel+7bad7e35a showing presets not populating correctly when switching between templates
• Jullian also observed that for normal users (non-admin view), the preset may never appear until the page is refreshed
• Network logs show different behavior on newer versions (only invoking external-auth)
• The UI has changed quite a bit between versions, but wonkiness still persists

Reference

See https://codercom.slack.com/archives/C094GRQG7UZ/p1761323173375519 for the original discussion and Loom video demonstrating the issue.