feat(web): track context source lift #372

Job	Run time
mutation	1m 41s
lint	1m 17s
Coverage (llvm-cov)	1m 31s
version	5s
cargo-deny (advisories + licenses)	24s
test (macos-latest)	39s
test (windows-latest)	48s
security	26s
test (ubuntu-latest)	41s
	7m 32s

Provide feedback