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](e20e7d6b-c6be-4a47-b132-672766f41421)

![grafik](d5b11b9c-c12f-4a29-8fb0-24e5aa511d18)

![grafik](d86bb444-36c7-426d-9cf1-c634963dffb1)

![grafik](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>
Conflicts:
	routers/web/repo/search.go
	templates/repo/home.tmpl
	templates/repo/search.tmpl
	templates/shared/repo_search.tmpl

services/context/pagination.go

@@ -53,5 +53,5 @@ func (p *Pagination) SetDefaultParams(ctx *Context) {
 	p.AddParam(ctx, "sort", "SortType")
 	p.AddParam(ctx, "q", "Keyword")
 	// do not add any more uncommon params here!
-	p.AddParam(ctx, "t", "queryType")
+	p.AddParam(ctx, "fuzzy", "IsFuzzy")
 }