Late 2013 Macbook Pro Super slow

I don't see any of the normal software issues which would cause any problems, but you have also omitted some sections of the EtreCheck report.

Your new SSD is very slow though. While I have seen one or two other people use a Timetec SSD on this forum, I don't recall or know anything about that brand. While the Timetec SSD is shown as an NVMe SSD it is not running at advertised speeds. Oddly, it is only running at SATA II speeds which max out at around 250MB/s. Something is really wrong here. The Etrecheck report is reporting the SSD connection at 5GT/s (or 5Gb/s which is approximately 500-700MB/s). The Timetec for Mac NVMe SSD product page shows this SSD should be capable of 1,000MB/s writes & 1,950 MB/s read speeds although on a macOS boot drive you will more often see write speeds cut in half in the EtreCheck report.

I suspect your new SSD is at fault, but the Logic Board could also be at fault. All things being equal, the SSD is usually the weakest link assuming no accidental liquid damage has occurred.

Of course, the problem could be with the Logic Board and/or the Battery. Power related issues can cause the laptop to run at slow .... even idle speeds which will cause very poor performance. There is no guarantee the SSD was ever the problem.

To help figure things out, you can try installing macOS onto an external USB3 SSD & boot from that external SSD to compare results. If booting from an external SSD is better, then the Timetec SSD is most likely at fault although the Logic Board's support circuitry for the SSD could be bad. If booting from an external USB3 SSD has the same performance issues, then most likely you have a Logic Board failure (or possibly a power/battery issue). It is best if the USB3 SSD supports UASP for optimal performance of USB3.

You can try checking to see if the CPU is being throttled. Run the following command from the Terminal app to see if the CPU is running at 800Mhz or at 2Ghz while performing tasks....viewing a YouTube video should definitely cause the CPU to run above 800Mhz. If the CPU frequency is stuck at 800Mhz, then it indicates the CPU is throttled for some reason....most likely a power related issue since you are not reporting the fans running at high speed. A power related issue can also be caused by the Logic Board, possibly the battery, or from liquid damage.

If the CPU is running above 800Mhz, it still does not mean everything is Ok since I have seen some Macs run at 2Ghz, but are extremely slow.....always has been due to some unknown Logic Board issue....most times associated with accidental liquid damage.

sudo  powermetrics  -s  smc  |  grep  -i  'system average'

This command will prompt you for your admin password. Nothing will appear on the screen as you type the password, so press the "Return" key to submit the password. This command will keep running until you press Control + C within the open Terminal window running this command.

FYI, here are instructions for posting an EtreCheck report:

How to use the Add Text Feature When Post… - Apple Community