There's no process for buying a laptop for an open-source dev who's code the business depends on but who is not an employee, so especially in German companies, you don't do that.
You would usually proceed as a donation from inventory or you'd give them some type of credit for purchase (might come off the marketing dept)
When donating something never go with the more expensive option (in this case, actually going and buying something you make on the market)
From a corporate accounting perspective, a "purchase" is "we pay money and we get a thing". Sometimes the thing needs to fit a stereotype; "a hardware", "a service", "a contract", but the dance is the same; request a quote, get a quote, place an order, get an invoice, pay the invoice, get a receipt, get confirmation of delivery.
Iff the transaction fits that mold, then it's generally straightforward. If it doesn't, then you need to find someone with the power to override the organisation; in an organisation resistant to internal tampering ("corruption") that can be quite difficult.
I wish we could just buy licenses sometimes ... I really hate fucking around with procurement processes