Refactor my-participating-studies-section.tsx: Implement backend API for participating studies

[coderabbitai]

Context

This component is currently a temporary implementation that needs refactoring once a proper backend API becomes available.

Related PR: #370
Comment discussion: #370 (comment)
File: src/components/section/my-participating-studies-section.tsx

Current Implementation

The component currently:

• Fetches all studies via useGetStudies (paginated, but fetching 100 items)
• Fetches user's participating study list via useMemberStudyListQuery
• Creates a Set of participating study IDs client-side
• Filters the complete study list against this ID set on the client
• Limits to 3 studies for display

Problem

• Performance concern: As the number of studies grows, fetching and filtering all studies client-side becomes inefficient
• Data type mismatch: The participating studies list and full studies list have different data structures, requiring this workaround
• Network overhead: Unnecessary data transfer for studies the user isn't participating in

Proposed Solution

Implement one of these backend API improvements:

Option 1: Batch fetch by IDs

GET /api/v1/group-studies/by-ids?ids=1,2,3&classification=GROUP_STUDY

Returns full study details for the specified IDs only.

Option 2: Enhance existing endpoint

Modify getMemberStudyList to return all information needed for StudyCard rendering, eliminating the need for a second API call.

Next Steps

• Backend team implements appropriate API endpoint
• Refactor component to use new endpoint
• Remove or optimize client-side filtering
• Consider whether this feature should remain permanent or be removed

Notes

• This feature may be removed in the future depending on product decisions
• Component should be treated as temporary until refactoring is completed
• Requested by @seong-jin-jo