make /projects searchable by project name

[AKolenda]

Problem

• There's no search function to find a project in the projects tab. Once you have a decent amount of projects you're just scrolling the whole table to find one
• related: Performance with several clients or projects #1138 was about someone with 2500+ projects, pagination helped but you still can't find a specific project quickly

Requested feature

• add a search input on the projects page, next to the filter button
• filters the table by project name as you type

Example

• same style as the "Search for a Project..." inputs that already exist in the project dropdowns

Expected behavior

• type part of the name -> table only shows matching projects (case insensitive)
• clear it -> full list is back

How I'd implement it

• client side only, in Projects.vue. The page already loads all projects and filters them in a computed (status/visibility/client), so the search is just one more condition in the same place
• reuse the input styling from the dropdown search so nothing new design-wise
• no backend/api changes
• roughly 20 lines + a playwright test

Would open a PR for this if the approach is fine