Refactor e2e test triggering to use path-based filtering

[VGau]

Description

Refactor e2e test triggering to use explicit path-based filtering. E2e tests run only when source files change in key paths, and skip when only test/doc files are modified.

Motivation

• Reduce unnecessary e2e test runs (saves CI time/cost)
• Clearer, maintainable filtering logic

Tasks

• Simplify get-has-changes-requiring-e2e-testing.yml with dorny/paths-filter
• Add post-filter evaluation to exclude test/doc files
• Remove unused inputs from main.yml

Acceptance criteria

• E2e tests run when source files change in included paths
• E2e tests skip when only test files (.test.ts, .spec.ts, _test.go) changed
• E2e tests skip when only doc files (.md, .mdx) changed
• E2e tests run when both source + test files change together