chore: QoL changes for Omnichannel (#31468)

apps/meteor/app/livechat/imports/server/rest/departments.ts

apps/meteor/app/livechat/imports/server/rest/inquiries.ts

...app/livechat/server/business-hour/AbstractBusinessHour.ts

apps/meteor/app/livechat/server/lib/Departments.ts

apps/meteor/app/livechat/server/lib/Helper.ts

apps/meteor/app/livechat/server/lib/LivechatTyped.ts

apps/meteor/app/livechat/server/startup.ts

...ee/app/livechat-enterprise/server/business-hour/Helper.ts

.../app/livechat-enterprise/server/business-hour/Multiple.ts

...ivechat-enterprise/server/hooks/addDepartmentAncestors.ts

...t-enterprise/server/hooks/afterForwardChatToDepartment.ts

...livechat-enterprise/server/hooks/afterRemoveDepartment.ts

...prise/server/hooks/onLoadForwardDepartmentRestrictions.ts

apps/meteor/ee/server/models/raw/LivechatDepartment.ts

apps/meteor/lib/callbacks.ts

apps/meteor/server/models/raw/LivechatDepartment.ts

apps/meteor/server/models/raw/LivechatDepartmentAgents.ts

apps/meteor/tests/end-to-end/api/livechat/04-dashboards.ts

...odel-typings/src/models/ILivechatDepartmentAgentsModel.ts