The implementation follows the MCP specification for filtering capabilities:

Server Capabilities: Servers can now declare support for filtering with the filtering capability, including whether list change notifications are supported.

Group Primitive: Groups are collections of tools that separate the server's toolspace by functionality or use case.

Tag Primitive: Tags are labels that can be attached to tools to denote cross-cutting concerns like status or operational safety.

Filter Parameter: The tools/list method now accepts a filter parameter that allows filtering tools by groups and tags.

Tool Definition: Tools can now be associated with groups and tags, which are included in the tool definition.

The implementation is fully backward compatible - if the filter parameter is omitted, all tools are returned as before.

In src/types.ts
* Added a new filtering capability to the ServerCapabilitiesSchema to allow servers to declare support for filtering groups and tags
* Created new schemas for groups and tags:
GroupSchema: Defines a group that contains tools, with name, title, and description
TagSchema: Defines a tag that can be attached to tools, with name and description
* Extended the ToolSchema to include optional groups and tags properties
* Added a ToolsFilterSchema to define filter parameters for the tools/list request
* Extended the ListToolsRequestSchema to include the filter parameter
* Added new request/response schemas for group and tag operations:
ListGroupsRequestSchema and ListGroupsResultSchema
ListTagsRequestSchema and ListTagsResultSchema
* Added notification schemas for group and tag list changes:
GroupListChangedNotificationSchema
TagListChangedNotificationSchema
Added type exports for all the new schemas

In src/client/index.ts

Added client-side methods to support the new filtering capabilities:

* Added imports for the new types and schemas
* Implemented listGroups() method to request a list of groups from the server
* Implemented listTags() method to request a list of tags from the server
* Updated the listTools() method to properly handle the filter parameter

In src/server/mcp.ts

Added server-side implementation for filtering capabilities:

* Added imports for the new types
* Added registration of the filtering capability in the McpServer constructor
* Added storage for registered groups and tags with _registeredGroups and _registeredTags properties
* Implemented request handlers for groups and tags:
  - setGroupRequestHandlers() for handling group-related requests
  - setTagRequestHandlers() for handling tag-related requests
* Updated the ListToolsRequestSchema handler to support filtering by groups and tags
* Extended the RegisteredTool type to include groups and tags
* Added methods to send group and tag list changed notifications:
  - sendGroupListChanged()
  - sendTagListChanged()
* Added methods to register groups and tags:
  - registerGroup(): Registers a group with name, title, and description
  - registerTag(): Registers a tag with name and description