I just checked the recent Windows updates in your Speccy url and you are still running 1803 so it is not the latest major update that has caused the sudden lag, btw, there is no indication that the latest major update has tried but failed to install, you could wait and see if things improve once you are running 1809.
Please run the Crucial system scanner tool on your notebook, this will confirm whether or not your computer can handle more than 8GB of RAM, if it is, please see below, if it is not, please advise, we are doing this because even though your computer has 2 memory slots some OEM/Brand name computers can only recognise a max of 8GB of RAM, in this instance 2 Xs 4GB sticks of RAM would be the only way of achieving dual channel and maximum capacity.
Your notebook has two memory slots so you can add a second stick to get you dual channel performance, you will see a marked improvement by doing this, for most users 8GB** of RAM is plenty so I will just suggest the least expensive upgrade that I would do if me Crucial CT51264BF160BJ 4 GB (DDR3L, 1600 MT/s, PC3L-12800, Single Rank, SODIMM, 204-Pin) Memory guaranteed to be 100% compatible by Crucial or your money back.
There is a less expensive 2GB stick option here but they want almost £5.50 P&P which bumps the price up to £18.80, there is also no guaranteed to be 100% compatible or your money back promise.
P S, how to i go about the partition thing you were on about?
It depends, because the notebook is circa 2013/2014 any recovery partition on the notebook will be eithers Windows 7 or 8 and not Windows 10 which you are presently running, you could leave that partition as it is on such a large storage capacity HDD and then partition what is left on the drive, couple of things below that you would need to do first.
1: If you do not already have Windows 10 media on disk or USB you need to create it either by burning it to disk or by downloading it to an 8GB or above USB thumbdrive, all that you need to know from here
2: Back up any important data,
3: Download and save to a USB thumbdrive all drivers that you need, make sure that they are for Windows 10 64-bit
4: Install Windows 10 and the HP system drivers.
5: Get Windows 10 and Windows Defender fully up to date then post back with an update for us, please do not install anything else until we have helped you partition the HDD.