Provide a machine-readable JSON representation of the `but base check` command so callers can programmatically consume base branch info, upstream commits and branch mergeability status. Introduce serializable structs (BaseCheckOutput, BaseBranchInfo, UpstreamInfo, UpstreamCommit, BranchStatusInfo), fetch the data before deciding output mode, and serialize the gathered data (base branch details, upstream commit list and count, branch statuses, up_to_date and worktree conflict flags). The human-readable output path is preserved.
replace emoji output with styled text for status messages

Update human-facing terminal messages to use styled text instead of
emoji glyphs. Replace "✅ Everything is up to date" with a bold green
"Everything is up to date" string, replace the uncommitted-changes
warning emoji line with a bold yellow "Warning: ..." message, and
replace the "🔄 Updating branches..." line with a bold "Updating
branches..." string.
Split base.rs into base/mod.rs and base/json.rs

Move JSON serde structs into a dedicated json.rs module to separate concerns and improve organization. The JSON output structs (BaseCheckOutput, BaseBranchInfo, UpstreamInfo, UpstreamCommit, BranchStatusInfo) were moved and made pub(super) so mod.rs can access them. The old base.rs file was removed.
Use ANSI colors for 'but base check' output

Replace emoji-based output with ANSI colored text for clearer, more
professional terminal display. Base branch names are shown in cyan; the
upstream count is yellow for >0 and green for 0. Commit SHAs are yellow
with descriptions dimmed. Status indicators are now textual tags with
color: [ok] green, [integrated] blue, [conflict] red/yellow, and [empty]
dimmed. Headers are bold and labels dimmed for a cleaner visual
hierarchy. This improves readability and removes distracting emoji icons.
Fix upstream commit display in human output

Human-readable output for the "Upstream commits" section incorrectly used recent_commits, causing it to show recent commits instead of actual upstream commits. Change the code to use upstream_commits for the human output so both JSON and human-readable views consistently show only true upstream commits.
Use upstream_commits for base check JSON output

Fix the JSON output for the "but base check" command to report only actual upstream commits. The code previously used recent_commits (which lists recent commits regardless of whether they're new upstream commits), causing the reported count to mismatch the listed commits. Switched to upstream_commits so the commits array matches the behind count and reflects only new upstream commits.