Is it worth upgrading the CPU on your old laptop? Or should you buy a new one? Well, that depends entirely on the original specification of your old unit. For example, some laptops have the CPU soldered into the motherboard, which means it is simply impossible to remove them or upgrade them. There appears to be a trend in new laptops having their CPUs soldered on the board, this is because it is cheaper for the manufacturer to produce.
Another consideration is the generation of your CPU, for example, a 1st gen CPU wouldn't be worth upgrading as they are over 12 years old, whereas a 2nd or 3rd gen CPU is worth it due to more recent hardware capabilities. A 2nd gen CPU is still more than enough to run Windows 10, these CPU still performs fine when combined with an SSD and a large amount of RAM, despite being 9 - 10 years old!
For example, a 3rd gen i3 CPU with a compatible chipset that accepts an i5 or i7 slot would definitely be worth upgrading. However, if the unit in question only has 4GB RAM and a physical hard drive, the notice would be minimal. It is also worth noting that some motherboards have different chipsets, or limitations designed by the manufacturer to prevent CPU upgrades (a ploy to get you to pay more) this is often the case with certain brands. Some PCs also require BIOS or firmware updates in order to read more up-to-date CPUs, so ensure your laptop is definitely up-to-date before modifying them.
Ultimately, it is down to the individual to determine the cost vs new argument component before proceeding with an upgrade. For example, is it worth upgrading if the CPU in question is £100, and the technician is charging £70 to do it? When a new one at a similar spec can be procured for an extra £100? It is important to consider all options.