An SSD really is the solution. You believe it just speeds up boot time, but it does speed up nearly everything else too.

Your Webpage? Your Browser loads it, stores new data into the cache and stalls while waiting for the HDD. Or it knows elements are in the cache and stalls waiting for them.

You click on the application menu? You PC tries to load 20 icons, tiny amounts of data an SSD has ready in a microsecond. Your HDD takes a full second because the seek between the 20 places where the icons are on the HDD takes so long.

I have some very old PCs I manage (mainly for relatives) and one couple uses a Core 2 Duo E6400 which should be quite similar to your PC. This PC is very usable for daily browsing with Ubuntu 22.04, boot time is about 25 seconds, then about 10 seconds to load up ebay. (I admit I optimized boot time quite a bit) The other PC they have is even slower than that, I just do not remember the exact CPU right now. That one is even used for old browser games similar to candy crush.

Of course it is not what I would use given the choice. I want to compile code in seconds, watch videos in glorious 4k and play a 3D game from time to time. But for them it works perfectly well, so well that they deny my offers to upgrade them