1. Checked all logos, updated 3 of them to newer versions.
2. Remove `open-with-` infix on the editor logos to be consistent with
other files.

<img width="626" alt="image"
src="https://github.com/go-gitea/gitea/assets/115237/3b2d9486-6e0a-45c6-b0e4-d38dc4c0b118">

- Update all JS and PY dependencies minus `@mcaptcha/vanilla-glue`
- Adapt to eslint rule rename
- Regenerate all SVGs because of [new
optimizations](https://github.com/svg/svgo/releases/tag/v3.0.4) from
svgo.
- Tested mentions, mermaid, vue, api docs

Move `public/*` to `public/assets/*`

Some old PRs (like #15219) introduced inconsistent directory system.

For example: why the local directory "public" is accessed by
`http://site/assets`? How to serve the ".well-known" files properly in
the public directory?

For convention rules, the "public" directory is widely used for the
website's root directory. It shouldn't be an exception for Gitea.

So, this PR makes the things consistent:

* `http://site/assets/foo` means `{CustomPath}/public/assets/foo`.
* `{CustomPath}/public/.well-known` and `{CustomPath}/public/robots.txt`
can be used in the future.

This PR is also a prerequisite for a clear solution for:
* #21942
* #25892 
* discourse.gitea.io: [.well-known path serving custom files behind
proxy?](https://discourse.gitea.io/t/well-known-path-serving-custom-files-behind-proxy/5445/1)

This PR is breaking for users who have custom "public" files (CSS/JS).
After getting approvals, I will update the documents.

----

## ⚠️ BREAKING ⚠️

If you have files in your "custom/public/" folder, please move them to
"custom/public/assets/".

---------

Co-authored-by: 6543 <6543@obermui.de>
Co-authored-by: Giteabot <teabot@gitea.io>

The plan is that all built-in auth providers use inline SVG for more
flexibility in styling and to get the GitHub icon to follow
`currentcolor`. This only removes the `public/img/auth` directory and
adds the missing svgs to our svg build.

It should map the built-in providers to these SVGs and render them. If
the user has set a Icon URL, it should render that as an `img` tag
instead.

```
gitea-azure-ad
gitea-bitbucket
gitea-discord
gitea-dropbox
gitea-facebook
gitea-gitea
gitea-gitlab
gitea-google
gitea-mastodon
gitea-microsoftonline
gitea-nextcloud
gitea-twitter
gitea-yandex
octicon-mark-github
```

GitHub logo is now white again on dark theme:

<img width="431" alt="Screenshot 2023-06-12 at 21 45 34"
src="https://github.com/go-gitea/gitea/assets/115237/27a43504-d60a-4132-a502-336b25883e4d">

---------

Co-authored-by: wxiaoguang <wxiaoguang@gmail.com>