…11677)

Here are the steps that I followed to generate this PR

- Update the `default_version` in `.repo-metadata.json` here

https://github.com/googleapis/google-cloud-python/blob/eca60c3027820c97fc12590d0709b8fe3eb54034/packages/google-ai-generativelanguage/.repo-metadata.json#L14
- Work around the docs issue mentioned in
https://github.com/googleapis/gapic-generator-python/issues/1776 by
applying this change locally
- Build the `v1beta2` and `v1beta3` clients locally in a clone of
[googleapis/googleapis](https://github.com/googleapis/googleapis) using
`bazel build
//google/ai/generativelanguage/v1beta3:ai-generativelanguage-v1beta2-py`
and `bazel build
//google/ai/generativelanguage/v1beta3:ai-generativelanguage-v1beta3-py`
- Run the docker containers for the owlbot copy-code and owlbot post
processor
```
 docker run --rm --user $(id -u):$(id -g)   -v $(pwd):/repo   -v /usr/local/google/home/partheniou/git/googleapis/bazel-bin:/bazel-bin   gcr.io/cloud-devrel-public-resources/owlbot-cli:latest copy-bazel-bin   --config-file=packages/google-apps-script-type/.OwlBot.yaml   --source-dir /bazel-bin --dest /repo
 ```
 
```
docker run --user $(id -u):$(id -g) --rm -v $(pwd):/repo -w /repo
gcr.io/cloud-devrel-public-resources/owlbot-python-mono-repo:latest
```

I also had to fix a bug in synthtool for the owlbot post processing: googleapis/synthtool#1861. Without this fix, the [docs/index.rst](https://github.com/googleapis/google-cloud-python/blob/main/packages/google-ai-generativelanguage/docs/index.rst) file would list `v1beta2` as the default import instead of `v1beta3`.

Fixes #11676 🦕

This PR updates the post processor image to the latest one which is
`gcr.io/cloud-devrel-public-resources/owlbot-python-mono-repo@sha256:eeaeabb180cbcf1300469ae7621cc1dd24f06b48e4cd2962008bd5150c5f7c1e`.

The latest image includes the following fixes:
googleapis/synthtool#1861
googleapis/synthtool#1867

Run the following commands to obtain the latest sha256
```
docker pull gcr.io/cloud-devrel-public-resources/owlbot-python-mono-repo:latest
```

```
partheniou@partheniou-vm-3:~/git/google-cloud-python$ docker inspect --format='{{.RepoDigests}}' gcr.io/cloud-devrel-public-resources/owlbot-python-mono-repo:latest
[gcr.io/cloud-devrel-public-resources/owlbot-python-mono-repo@sha256:eeaeabb180cbcf1300469ae7621cc1dd24f06b48e4cd2962008bd5150c5f7c1e]
```