Yes, Copilot supports skills. Practically all agents support very similar feature sets or are actively building up parity support if not already there. The only real difference between systems is the prompt and payment method. Copilot even allows you to use Anthropic's own skills repository: https://github.com/anthropics/skills
https://docs.github.com/en/copilot/concepts/agents/about-age... details the support for skills. https://docs.github.com/en/copilot/concepts/agents/copilot-c... details the CLI tool in general, which seems more or less on par with Claude Code's.