Upgrade to 16GB anyway.

Yes. RAM is cheap, and the CPU bottleneck you’re worried about is probably not as bad as you think.

Your older CPU will still work fine for most tasks — browsing, Office, light gaming. The real bottleneck these days is usually having too little RAM, not an old processor. If you’re stuck at 8GB, jumping to 16GB will let you keep more tabs open and run background apps without swapping to disk. The CPU slowdown might cost you a few seconds; running out of RAM makes the whole machine crawl.

The only case where I’d hold off is if you’re on something really ancient — like a Core 2 Duo or first-gen i3 — and the RAM upgrade costs more than the computer is worth. Otherwise, 16GB gives your old CPU a fighting chance to stay useful for another year or two.

Future you will thank present you for not closing everything just to open a PDF.