`package.json` synchronizer assumes that all dependency version strings use a leading character

If the version string for one of the dependencies in your package is, say, `2.26.0` instead of `^2.26.0`, then the tool will crash when attempting to sync the dependencies.

See this line: https://github.com/MetaMask/template-sync/blob/294727e368f1120e79c29fa4039b2fcf49c95bb1/src/processing/package-json.ts#L64. I think we only need to take off the leading character if it is `^` or `~`.

Start at src/processing/package-json.ts, especially line 64, and inspect how dependency version strings are handled during synchronization. Reproduce the crash with an unprefixed version such as 2.26.0, then verify that synchronization succeeds for unprefixed versions while existing ^ and ~ versions continue to work.

Written by the indexing model from the issue text.