[PM-12092] fix: Add new item should set item type

[Chandra-Mauli-Sharma]

🎟️ Tracking

Add new item should set item type (https://github.com/bitwarden/clients/issues/10994)

📔 Objective

Selecting an item type to filter by and then clicking on + (Add new item) should set the item type of the new item.

📸 Screenshots

https://github.com/user-attachments/assets/2f0f4d7d-c16e-4adf-b802-9916c21296e1

⏰ Reminders before review

• Contributor guidelines followed
• All formatters and local linters executed and passed
• Written new unit and / or integration tests where applicable
• Protected functional changes with optionality (feature flags)
• Used internationalization (i18n) for all UI strings
• CI builds passed
• Communicated to DevOps any deployment requirements
• Updated any necessary documentation (Confluence, contributing docs) or informed the documentation team

🦮 Reviewer guidelines

• 👍 (:+1:) or similar for great changes
• 📝 (:memo:) or ℹ️ (:information_source:) for notes or general info
• ❓ (:question:) for questions
• 🤔 (:thinking:) or 💭 (:thought_balloon:) for more open inquiry that's not quite a confirmed issue and could potentially benefit from discussion
• 🎨 (:art:) for suggestions / improvements
• ❌ (:x:) or ⚠️ (:warning:) for more significant problems or concerns needing attention
• 🌱 (:seedling:) or ♻️ (:recycle:) for future improvements or indications of technical debt
• ⛏ (:pick:) for minor or nitpick changes