Webpack-bundled library broken in v6.2.0 only

In the Bigtable SDK v6.2.0, there is probably an incorrectly imported .proto file somewhere, which interferes with Webpack's bundling capabitilies. 6.1.0 works great, so this bug was introduced in 6.2.0. This is a big problem because we trust that minor versions are fully backwards compatible, so we have our build system automatically upgrade packages using the package.json ^ syntax. This broke a lot of our production builds. Even just importing the library without using anything throws the below error

```
webpack:///./node_modules/protobufjs/src/root.js?:118
throw err;
^

Error: ENOENT: no such file or directory, open '/workspaces/protos/google/bigtable/v2/response_params.proto'
at Object.openSync (node:fs:561:18)
at Object.readFileSync (node:fs:445:35)
at fetch (webpack:///./node_modules/protobufjs/src/root.js?:195:34)
at Root.load (webpack:///./node_modules/protobufjs/src/root.js?:231:13)
at Root.loadSync (webpack:///./node_modules/protobufjs/src/root.js?:275:17)
at Object.loadSync (webpack:///./node_modules/protobufjs/src/index-light.js?:69:17)
at eval (webpack:///./node_modules/@google-cloud/bigtable/build/src/client-side-metrics/operation-metrics-collector.js?:24:27)
at ./node_modules/@google-cloud/bigtable/build/src/client-side-metrics/operation-metrics-collector.js (/workspaces/gcp-bigtable-webpack-bug-reproduction/dist/index.js:139:1)
at __webpack_require__ (/workspaces/gcp-bigtable-webpack-bug-reproduction/dist/index.js:8004:42)
at eval (webpack:///./node_modules/@google-cloud/bigtable/build/src/client-side-metrics/metrics-config-manager.js?:17:39) {
errno: -2,
code: 'ENOENT',
syscall: 'open',
path: '/workspaces/protos/google/bigtable/v2/response_params.proto'
}
```

## Reproduction
I set up a minimum reproducable example on this Github repo: https://github.com/Joshua-Zou/gcp-bigtable-webpack-bug-reproduction?tab=readme-ov-file#reproducing.
It just requires a couple of steps:
1. Install NodeJS > 18 and NPM. I don't think NodeJS version impacts this bug.
2. In this directory, run npm install
3. In this directory, run npm run build
4. In this directory, run npm run start
5. Observe the issue. You can also go into package.json and change the version of Bigtable from 6.2.0 to 6.1.0, reinstall dependencies, rebuild, and start the program again. This will not cause the error to be thrown.