So basically, plug it in and get on with it?
I (using my one remaining braincell) got the requirement to be 360w IE 240v x 1.5a = 360w, did I get that wrong? or are the numbers on the charger more incomprehensible/complicated? it's the one thing I struggled with on my self build, fuses, cable sizes, not for the weak minded, work of the devil.
Basically, Yes
Though it is always worth double-checking something if in doubt.
As someone mentioned on the thread on the other forum, the 1.5A was for the lower voltage. The Adapter is a world-wide compatible one (for when you are cycling all over the place) and will take anything from 100V to 240V.
The Current quoted is the maximum possible amperage - and for a given Wattage, the maximum amps are always with the lowest Voltage (Ohms law ... P=IV, and also P/V=I. So (P=IV) 150W = 100V x 1.5A. Then (P/V=I) 150W/230V = 0.65A)
These input numbers tend to be worst-case transient surge numbers - What is best to look at really is the DC output as that makes more sense on just about all transformers. Yours says 24V @ 2A = 48W.
Add in losses in the transformer (say 25% as likely inefficient) and you will be pulling 60W from the AC supply (inverter or mains).
Add in Inverter losses (say another 25%) and you will be pulling 75W from the battery (about 6A on a 12V DC system).
The 12V sockets tend to be rated at 120W/10A (Your 12V dash socket might be like mine though? rated at 180W (although I don't think I would try it at that power!)) so you are within quoted parameters.
The biggest problem with those sockets can be the dreadful connection between socket and plug. Some plugs are just terrible; some sockets are not that good either (VW Transporter ones are unbelievable poor). Using an Anderson Plug setup in the future will give you a very reliable quick-connect.
What is worthwhile having I think is a some kind of AC Power Monitor such as one of these plug-in "watt meters" -
https://amzn.to/3u49gIe .
Plug this into the house AC socket, plug in your eBike Charger and battery and you will see the AC current drawn, the power in watts and also very interestingly the total Watt-Hours taken to charge the battery (can use for things like Laptop chargers as well for example).
Useful to know just how much that really takes to charge the battery and help you decide when to plug it in (you might find it is low enough to charge a bit without solar or driving sometimes?).
You would need to add 25% on top for inverter overhead though of course.