Tasks

1. Writer (openvidu-livekit)

1.1 Add the ref type to openvidu/analytics/projection/expr.go for field(), $$REMOVE and the $$this variables of the projection, and escape every other string starting with $ in stage(). Wrap the participant attributes in $literal. Verify with the unit tests of openvidu/analytics/... and the lint of the fork.
1.2 Add a writer integration test with a room, a participant and an egress whose values start with $. Verify with the analytics integration tests, the migration and contract suites included.

2.1 No CHANGELOG line: the analytics data model has not shipped. No AGENTS.md change. Verify by reading the change against both files.

3.1 Run the spec validation and the format check of the dashboard, and typings/contract/writer-check.sh against the fork. Verify that they pass.