Add tests for legacy `Backend` impl #5098

Job	Run time
Cargo fmt	17s
Check unused dependencies	26s
Cargo check (WASM)	1m 16s
Cargo clippy	1m 1s
Cargo check	1m 16s
Check documentation and run doc tests	1m 16s
Cargo clippy (WASM)	41s
Test (WASM)	1s
Test (Native)	1s
Test (Unstable Backend)	1s
Test (no_std)	1s
Test (Light Client)	1s
	6m 18s

Provide feedback