feat(chat): redesign publication filters (Issue #1640)

[Alexander-Kezik]

Description:

redesign publication filters

Issues:

• 1640

UI Changes:

https://www.figma.com/design/lwL5jneveZczAj5RLcLFH2/DIAL-Chat?node-id=9611-4262&t=5a91fUZl3J8DNkRN-4 https://www.figma.com/design/lwL5jneveZczAj5RLcLFH2/DIAL-Chat?node-id=9611-4385&t=5a91fUZl3J8DNkRN-4

Checklist:

• [x] the pull request name complies with Conventional Commits
• [x] the pull request name starts with fix(<scope>):, feat(<scope>):, feature(<scope>):, chore(<scope>):, hotfix(<scope>): or e2e(<scope>):. If contains breaking changes then the pull request name must start with fix(<scope>)!:, feat(<scope>)!:, feature(<scope>)!:, chore(<scope>)!:, hotfix(<scope>)!: or e2e(<scope>)!: where <scope> is name of affected project: chat, chat-e2e, overlay, shared, sandbox-overlay, etc.
• [x] the pull request name ends with (Issue #<TICKET_ID>) (comma-separated list of issues)
• [x] I confirm that do not share any confidential information like API keys or any other secrets and private URLs

[Alexander-Kezik]

/deploy-review

Environment URL: https://chat-ai-dial-chat-pr-1673.nightly-test.deltixhub.io E2E tests status: failed

[Alexander-Kezik]

/deploy-review

Environment URL: https://chat-ai-dial-chat-pr-1673.nightly-test.deltixhub.io E2E tests status: failed

[Alexander-Kezik]

/deploy-review

Environment URL: https://chat-ai-dial-chat-pr-1673.nightly-test.deltixhub.io E2E tests status: success

[denys-kolomiitsev]

/deploy-review

Environment URL: https://chat-ai-dial-chat-pr-1673.nightly-test.deltixhub.io E2E tests status: success