Going from a mechanical hard disk drive to a solid-state drive is going to be a massive uplift in system performance and usability. From a SATA SSD to an NVMe SSD, you will notice very little benefit from the latter except in certain specific tasks.
The reason is latency or the time to fully read or write a file from/to the storage device - in a hard drive this takes relatively long, in an SSD relatively little, and it comes from how these devices are physically constructed. Let's look at a very simplified example of how each of these devices would read a file.
For a mechanical HDD, it has to spin its platters to the location of the first part of that file (seeking). Then it has to read that part. Then it has to spin the platters to read the next part, and on and on until the entirety of the file has been read. If the file is large, and/or split over multiple locations (fragmented), the drive has to do more work, which takes more time. In this case, most of the time is spent by the drive looking for the file, not actually sending the file data to whatever asked for it - the latter gets the file data in drips and drabs until the drive is done, so you have to wait quite a while.
In contrast, a solid-state drive is able to access all the parts of a file almost instantaneously. But larger files will be too big to send at once, so the SSD has to chop them up and send the pieces out to whatever requested them, which is still much quicker than an HDD.
The only difference between a SATA and NVMe SSD is that the latter has more capacity to send that data (bandwidth) - so if you are reading a very large file, NVMe will be faster than SATA. Other than that they will generally perform similarly.
Therefore, there generally isn't any benefit from going from a SATA SSD to an NVMe one. But there is always a noticeable benefit from going from an HDD to either a SATA or NVMe SSD.