Add v0.1 server browse endpoints

[rdimitrov]

Summary

• The Desktop/FE team needs upstream-compatible server browse endpoints to align with the registry server's API. Currently servers are only available via the ToolHive-specific /api/v1beta/registry/{name}/servers endpoint which returns ToolHive types.
• Add v0.1 server endpoints that return ServerJSON matching the upstream MCP registry spec, with pagination and search. Combine with the existing skills endpoint into a single router with shared helpers.

Fixes #4199

Type of change

• New feature

Test plan

• Unit tests (task test)
• Linting (task lint-fix)

Changes

File	Change
pkg/api/v1/registry_v01.go	New: combined router + shared helpers (pagination, provider accessor, JSON errors)
pkg/api/v1/registry_v01_servers.go	New: list + get server handlers with ServerJSON conversion
pkg/api/v1/registry_v01_servers_test.go	New: integration + unit tests
pkg/api/v1/registry_v01_skills.go	Refactored to use shared helpers
pkg/api/v1/registry_v01_skills_test.go	Updated for shared router
pkg/api/server.go	Mount combined RegistryV01Router()

Does this introduce a user-facing change?

Yes — two new API endpoints:

• GET /registry/{name}/v0.1/servers (paginated, searchable via ?q=)
• GET /registry/{name}/v0.1/servers/{serverName}/versions/latest

Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 61.74497% with 57 lines in your changes missing coverage. Please review.
✅ Project coverage is 69.09%. Comparing base (e92dba4) to head (94ae593).

Files with missing lines	Patch %	Lines
pkg/api/v1/registry_v01_servers.go	49.42%	35 Missing and 9 partials ⚠️
pkg/api/v1/registry_v01.go	78.57%	11 Missing and 1 partial ⚠️
pkg/api/server.go	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #4871      +/-   ##
==========================================
+ Coverage   69.06%   69.09%   +0.03%     
==========================================
  Files         531      533       +2     
  Lines       55172    55264      +92     
==========================================
+ Hits        38104    38185      +81     
- Misses      14140    14142       +2     
- Partials     2928     2937       +9     

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