It is okay for you to call this a laptop from the 'stone age'.
But it is NOT okay to say you'll get a half decent laptop with NVME.
This laptop may not be blazing fast by today's standards, but it is fast enough, especially for the work I do. How often do you make use of NVME speeds and how much time does that save in actual day-to-day use?
I wasn't trying to argue against that. The point is that you might not be able to transfer a 2.5 inch SATA SSD to your new laptop that you probably will end up buying sooner or later, especially if it will be later rather than sooner, excepting only if you can live with using this SSD externally later. That's right... "good" laptops with internal 2.5 inch drive bays are already slowly but surely getting harder to come by, or at least you will have limited choices if you decide to wait too long, possibly you will need to pay extra, like, for example, if you will be forced (in a certain sense) to buy one that, while still being new and unused (or maybe), uses older tech so that the total value for money may in fact be lower as opposed to be higher. But your current laptop has no M.2 socket, so as a result from that, if you can NOT live with the potential problem described above, then you will be forced to look for an external solution, in which case it will be possible to opt for an M.2 NVMe USB enclosure (that can already be had for less than $20), i.e. with an NVMe SSD in it. And that can later be transferred to a newer laptop, either externally or internally, and without having to worry as much about any performance related factors so you'll gain the advantage of a wider flexibility in pure terms of future upgrade possibilities─and at a relatively small extra cost, also in addition to that. Like it or not... trying to squeeze several more years out of a 2013 laptop will be always a big gamble, and that is putting it mildly. But hey, it isn't MY money to burn. People should buy whatever it is that they want to buy, so if you really feel like doing an
internal 2.5 inch upgrade anyway after all, then by all means go for it. I am just saying I would never do that, and why.
I don't think it makes nearly the same difference as an SSD makes over an HDD. I'm talking of real world use, not just benchmark tests. SATA SSDs are fast enough for routine use, even by today's standards.
Up until the beginning of 2018, I didn't even own an SSD, and that is in spite of the fact that people on Sevenforums had been saying for more than 8 years that it is impossile to live without one. So how did I do it, then? Simple. For the most part, putting the laptop to sleep instead of shutting it down, and using Diskeeper in concert with Romex Software Primo Ramdisk (with the Dynamic Memory Management option enabled) was how.