Method: identify the exact context your input lands in, then craft the payload that breaks OUT of that context. Prove execution by making your injected JavaScript call /m03/api/solve/attr_noangle (e.g. with fetch()). No external collector needed. Server-rendered sinks also auto-mark once a value that would run is reflected/stored here.
< and > are HTML-encoded, so you cannot introduce a new element - but the quote character is not filtered. Stay inside the existing element and give it behaviour it should not have.