IT/HR will have a procedure and give you instructions.
Best case someone will pick everything up. Or you'll have to arrange shipping yourself. In any case they'll need to pay for it, and as long as you packed reasonably/followed instructions it's their problem if something is damaged or lost in transit.
How they get their laptop back is their problem. Just ask them.
But to answer the topic question, it seems that a recently-made-popular strategy is start on the newer job and keep the older one in low-priority mode until you get fired for low performance. Apparently it might take years depending on how the environment allows you to coast. But I wouldn't do that, and this may be illegal to do depending on your specific situation, jurisdiction and contracts.
I know there a few companies that have popped up to handle this exact issue, one of them being https://helloretriever.com. From what I know they handle sending you the prepaid box and shipping it back to your employer.
At the end of the day though its the company's issue so let them take the lead on it.
I guess someone sends you a fedex box, and you just drop it at a fedex location
Back when we were in lockdown, I passed it to a HR representative who was in my area. In some past jobs, they let me keep the device even though I offered to buy it from them. It depends on the policy.
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Ask your manager. In our company, we ask people to ship it back with insurance (we pay for it of course).