feat(backends): add Beads (bd) storage backend

[RooseveltAdvisors]

What

Implements the existing pluggable Store seam (src/store.ts) for the Beads issue tracker: a second backend alongside markdown, selected via .tasks.toml backend = "beads".

Why

We run agent fleets where the dispatch pipeline (fm-spawn, session-start, backlog handoff) calls tasks-axi, while task truth lives in a Beads graph (Dolt-backed, dependency edges, bd ready). The adapter removes double bookkeeping: one CLI surface (tasks-axi), pluggable storage (markdown or beads). Our fleet has been running it in production across ~25 agent homes for the last day.

Design notes

• ID preservation: tasks-axi slug ids map 1:1 to bd issue ids via bd create --id (bd rejects ids outside its prefix; we validate before invoking). No sidecar mapping needed.
• Post-call verification: transitions/deps verify the requested result against bd's actual response, not mere task existence - a silently no-oped update surfaces as an AxiError.
• Holds: map to a tasks-axi-held label; hold.until mirrors native --defer; clearing uses bd's documented clear operation.
• Dependency reasons: bd has no native edge-note field, so reasons persist in a versioned base64url metadata header (tasks-axi:beads/v1) in the issue description; same header carries kind/repo and archived-body bookkeeping.
• Timestamps: native bd created/closed timestamps are used (no preservation encoding - deliberate ponytail cut).
• Capabilities: deps=true, fullTextSearch=true, comments=true, customStates=true, serverMintsIds=true, publicFollowups=false, prune=false.
• markdown backend untouched: deriveLinks was extracted to shared src/links.ts (net negative lines); markdown behavior and tests unchanged.

Testing

353 lines of fixture-mocked tests: CRUD round-trip, transitions with post-call verification, dependency add/remove with reason encoding, prefix rejection, bd's structured missing-issue shapes, hold persistence and dated-hold clearing, config resolution. Full suite green.

Config

backend = "beads"

[beads]
path = ".beads"        # .beads directory (or its parent)
binary = "bd"          # bd on PATH
prefix = "bd"          # expected id prefix for slug validation

[LeonidShamis]

Please check PR #52 - it looks like we worked on the same feature

[RooseveltAdvisors]

I checked PR #52. It is a second, overlapping Beads backend implementation (with a different config shape plus mirror, prune, and real-bd conformance work), not an unrelated change. Both PRs cannot be applied independently without overlap. Since #52 is still open and there is no explicit supersession or rejection signal, I’m leaving #53 open pending your direction on which implementation to keep.