Delivery includes the Logitech Crayon stylus and associated documentation. No other accessories are mentioned in the official delivery contents. The pen is rechargeable and uses a USB-C or Lightning connector, depending on the version, but the charging cable is not explicitly mentioned as being included in the box.
Gemäss Logitech ist die Spitze als Ersatzteil erhältlich (https://www.logitech.com/de-ch/products/ipad-accessories/crayon-ipad-digital-pencil.914-000034.html#specs-support)
This item should be compatible with the 3rd and 4th generation. The Ipad Air 2022 seems to be 5th generation.
This one should be compatible: Zagg Pro Stylus
According to the manufacturer, the is only compatible with iPads from 2018: Pixel-perfect digital drawing pen for all iPads (all models from 2018) All iPad models must be updated to iOS 12.2 or higher.
Personally, I think you can draw much better with the Apple Pencil, because the Logitech Crayon doesn't recognise the different thicknesses. Otherwise, you hardly notice any differences, and the Crayon feels relatively good in the hand.