The path mismatch is the part I'd keep: Claude Code looks in .claude/skills, and the assistants you switched to were looking in .agents/skills, so Vibe never saw the skills you'd already written.
I'd also keep the practical fix. Put the shared skills in ~/.agents/skills and ./.agents/skills, move anything already in the Claude folders first, then symlink the Claude paths onto them so you are not maintaining two trees.
One small addition after the symlink: start a fresh session in each tool and confirm a skill you know by name actually appears. If an old .claude/skills folder was left in place instead of replaced, the shared skills can still go unseen, and that check is cheaper than finding out mid-task.
Have you found any assistant that still ignores .agents/skills even after the symlink, or does that cover the set you use?