Build process is outdated

In order to achieve standardization with our other libraries, we should:

- Remove `browserify` as a dependency
- Add `tsup` as a dependency (copy version from module template)
- Remove `build.sh`
- Add the `build:types` package script (copy from module template)
- Update the `build` package script to use `tsup` to compile the TypeScript code to JavaScript and `tsc` to create TypeScript declaration files.
- Rename the `typings` field in `package.json` to `types`
- Add `exports` field to `package.json` (copy from module template)
- Add `module` field to `package.json` (copy from module template)
- Add `sideEffects` field to `package.json` (copy from module template)
- Remove trailing slash from `dist/` in `files` field

Start by comparing package.json with the module template, then inspect build.sh and the current package scripts, dependencies, and package metadata. Done means the listed browserify/build.sh changes, tsup-based build scripts, and package.json fields match the template and the project build completes successfully.

Written by the indexing model from the issue text.