How to upgrade my HP notebook HDD to SSD

I am a non-technical person living in Italy. I have an old HP notebook of 2013 (mod. Envy 15-j040el) with 12 GB RAM and 1 TB HDD. Since my laptop has become painfully slow, I was wondering whether an upgrade of my legacy HDD to a compatible SSD would solve the slowness problem.
However, I must clarify that the HP laptop originally came with Windows 8 Home 64 bits, which was later upgraded to Windows 10 (Version 22H2 [OS build 19045.4239]). Would a simple cloning of my HDD on an SSD (Crucial BX500 1tb 3d nand sata 2.5) solve my problem, or do I need to install Windows 10 separately?
Could someone advise about how to go about cloning; and if Windows 10 needs to be installed separately, how to do it?

You'll have to learn about disks and partitions, and possibly about the Windows 10 Recovery Partition and WinRE. I don't know what's the problem with cloning to smaller targets (provided that there's enough free space in the source), although you wouldn't do such unless the original disk has say 940 GB and the target 930 GB (neither of them have 1024 GB, regrettably). The Recovery Partition position matters, possibly the problem is there. But you could disable WinRE, clone, and enable WinRE. And if cloning to a smaller target is a problem, adjust the original partition sizes, shrinking C: and moving the Recovery Partition to the left if it's at the right. For a more detailed plan you need to install a "friendly" utility like MiniTool Partition Wizard or Aomei Partition Assistant, and post screenshots here if you want.

When Windows partitions weren't so messy as they're nowadays, with a new HDD or SSD you got a tool for doing the cloning. Can't these tools solve these problems automaticly?

An alternative to "cloning" is "imaging": generating a very big file that has inside all the contents of a hard disk or a partition. You would do it in two steps: generating the image first and restoring it second. Both options (clone and image-restore) are done by the same kind of software (for instance Macrium Reflect or Acronis True Image). This software can restore images to smaller targets (I've a lot less experience with cloning) provided that the contents still fits, for instance from a 1000 GB source with 700 GB free (so it has 300 GB worth of data) to a 500 GB target (that would end up with 200 GB free after the operation).

You would need a 3rd "disk" for this, but instead of buying other one, you could partition your source (shrink C: + move Recovery Partition if needed + create new empty partition), create an image of your current 3 or 4 Windows partitions in the newly created one (with compression I'm getting 55% sizes -each original 100GB generate 55GB in image size-, so you would need that the original drive has somewhat more than 1/3 free for the image), restore it to the new drive, detach the ancient drive and enjoy the new SSD.