fix: fix rendering bubbletea v2 regressions for local install

[amoeba]

This fixes two regressions in bubbletea v2,

1. tea.Println inside Update() breaks scrollback
2. If a subcommand with a TUI (i.e., install) returns too quickly, bubbletea runs into a timing issue between switching between cooked and raw mode. I think bubbletea starts in cooked mode, switches to raw mode while showing the TUI (i.e., during prog.Run()), and switches back to cooked mode after. prog.Run() starts and stops so quickly when we run dbc install on local archive that some terminals haven't sent their terminal probe response before bubbletea switches back into cooked mode so the probe response shows up.

The fix for (2) was LLM written so a review there would be good.

This PR is split into separate commits so when you review this, you'll need to find a terminal that reproduces the issue (Ghostty, iTerm2, WezTerm I think too) and then work through the commits one by one to see the fixes. Issues (1) and (2) above are fixed by separate standalone commits.

Closes #351

[amoeba]

Hey @zeroshade, could you take a look at this, specifically if you can reproduce the original two issues and verify each of the fixes.

[zeroshade]

I was able to reproduce the issues and verified the fixes. Nice! Thanks!