Reduce remaining setup_common Bash temp and diagnostic helper surface

[codeforester]

Problem

cli/bash/commands/basectl/subcommands/setup_common.sh still has remaining maintainability hotspots after the earlier project-routing and JSON-formatting reductions:

• Manual cleanup remains around temporary files even where std_make_temp_file and std_make_temp_dir are available.
• Check-result collection still carries shell-side result-file parsing and aggregation that should be kept narrowly bounded.
• The file is large enough that new setup/check changes need clearer helper boundaries and cleanup conventions.

This issue is not a request to split setup_common.sh by topic. The existing ownership note is still right: reduce ownership only where the boundary is clear and testable.

Scope

• Replace remaining manual temp cleanup with existing base-bash-libs cleanup helpers where safe.
• Tighten the setup/check result helper boundary without changing user-visible check, doctor, or setup behavior.
• Refresh ownership notes if the current docs are stale after the change.

Acceptance Criteria

• Temporary paths created through std_make_temp_file or std_make_temp_dir rely on registered cleanup unless immediate deletion is required for semantics.
• Existing setup/check/doctor output and exit behavior are preserved.
• Focused setup/check tests and the broader Base validation gate pass.