I know longer use this forum, but I have been asked by a member to comment on your problem. I tried sending a PM but you apparently do not allow them.
I have just had the very same noise, as your video clip shows, fixed, by having the gearbox bearings replaced. The way to check the input shaft bearing is, with the engine running and the car in neutral and stationary, depress and release the clutch pedal. If the noise is there with the pedal released and goes away when the pedal is depressed then it is the input shaft bearing which is faulty. The only part of the gearbox which is rotating at this time is the input shaft. This is a common fault with GD models of the Jazz. I was assured that it gets worse but does not lead to a transmission failure. I ran mine for several thousand miles before the noise became unbearable. At first it only seemed to be noticeable in first gear, but then started to make its presence felt further and further up the gears. Sometimes it would disappear completely for 20 or 30 seconds (which was even more worrying!).
I got quotes from a garage who had a Honda trained mechanic and from a couple of transmission specialists. The Honda mechanic said the box had to come out and be stripped on the bench, at a cost to repair of £1000. The transmission specialist who did the job said they could do it in place at a cost, including all seals and bearings (he said it was pointless stripping it down and only replacing the input shaft bearing), of £324. The car is now like a new vehicle.
I do not think an amateur could do it in situ (or a garage who only did the repair occasionally). The transmission specialist said they do them regularly (one or two a week), and I imagine he had specialist tools, such as dummy shafts, temporary open housings and the like.
You mention the release bearing. The release bearing only makes a noise as you first start to depress the pedal and goes away once pressure is applied. It is quiet with the pedal released (I did a huge amount of research, as you may gather).
As I said earlier, I no longer follow this site, but if you have any further questions or comments, for me, personally, you can PM me. The administrator sends a copy of any PMs to my personal email account