Cranking sounded “odd”. But if you say it started and idles fine now then it’s probably not a timing issue. So, no, a compression test is not needed.
Some engines have separate timing chains for each exhaust cam and if one breaks the engine can still run on 3 cylinders. I’ve heard it on an engine that was run out of oil until an exhaust cam seized. It cranked a lot before starting and it didn’t run well at all. Maybe someone knows if this one has that kind of timing chain setup. It would be too much of a coincidence though for the fuel pump and the timing chain to both break. The cranking did sound strange like at least one cylinder had low compression. Maybe it’s a stuck or burnt valve.
What else could that hissing sound be other than exhaust back pressure and a clogged catalytic converter? Did anyone hear how after it ran briefly in the video that the cranking was slower afterward? I know some cars have a small pre cat up by the engine, one for each exhaust manifold. Maybe one of those has clogged (on 3 cylinders only) causing the uneven cranking sound?
Yes those do help. If you had a broken or slipped timing chain, it would be on only 3 cylinders, which would mean that the engine would still run.
But with that gas leaking out sound and the slow cranking after it ran briefly I’m thinking you have a clogged exhaust system.
Could be running rich which ruined the catalytic converter.