Unify search boxes (#29530)

Unify search boxes (#29530)

Unify all but a few search boxes to use uniform style, uniform
translations and shared templates where possible.
Remove a few duplicated search templates, e. g. code search.

<details><summary>Example after screenshots:</summary>

![grafik](https://github.com/go-gitea/gitea/assets/47871822/e20e7d6b-c6be-4a47-b132-672766f41421)

![grafik](https://github.com/go-gitea/gitea/assets/47871822/d5b11b9c-c12f-4a29-8fb0-24e5aa511d18)

![grafik](https://github.com/go-gitea/gitea/assets/47871822/d86bb444-36c7-426d-9cf1-c634963dffb1)

![grafik](https://github.com/go-gitea/gitea/assets/47871822/a76c0319-0518-484a-a840-563d02b61198)

</details>

Also includes #29700

Co-authored-by: 6543 <6543@obermui.de>
---------

Co-authored-by: 6543 <m.huber@kithara.com>
Co-authored-by: 6543 <6543@obermui.de>
Co-authored-by: silverwind <me@silverwind.io>
Co-authored-by: Giteabot <teabot@gitea.io>