Were you using satnav ? There have been big changes in traffic arrangements to cater for the new cross-city tram route via Cross St.
Essentially you drove into Hunts Bank from the wrong end, as almost all of it is a one-way street for traffic except buses. If you'd entered via Victoria St, you'd have been OK.
You drove in off Corporation St, and before turning would have been presented with one of these two signs depending on your approach: -
From the north
https://maps.app.goo.gl/LCESuFWFzneDTKHbAfrom the south
https://maps.app.goo.gl/QKqD5eAPyHRs1X6o7Then driving down the 100 yards open for traffic, you'd have come to the bus lane sign on the left, and a No Entry sign to the right, which is there for the one-way traffic lane. At this point your passenger would have been in easy walking distance from Victorian Station, and you could have dropped him off, turned round, and driven out the way you came in. Any reason why you didn't do this ?
https://maps.app.goo.gl/7zgy1ZybLCg5RHYD9So the contravention would seem to be made out, although their video doesn't show you passing the signs. However if you decided to appeal on that, the council will respond with library pictures and a statement. Adjudicators decide using the civil law test of "on the balance of probabilities", so for me, this is not a winner.
As regards the PCN itself, I see no errors of content in it that would be fatal to its enforcement, but others may do. In 2022, the Act under which bus lanes were enforced outside London changed over to the Traffic Management Act, (see top of your PCN). The change did catch out some councils and made their PCNs void , but I suspect the Manchester ones are OK. If there is a flaw then no doubt somebody on here will point it out.
I suggest you submit representations on a fairly humble basis explaining the circumstances as you have here and explain that you normally never drive in Manchester city centre, having always used public transport, but the circumstances of the evening gave you no choice but to use your car to assist your friend.