If I'm not mistaken, you are not installing a battery or the battery died.

I notice that Mac laptops since PowerPC time has got a firmware settings that only allowing the performance to runs at half speed when there's no battery installed. I learned about this in macrumors forum in the PPC section.

It happens to my 2006 Macbook Pro 17", for many years I thought it's not running well until I read this somewhere. It was running around 1+ Ghz until I install a new battery and now it's running at 2.16Ghz.

Hope this helps.

Btw, I have the same laptop and I've upgraded to 16GB rams. Also I have 500GB Samsung Evo 850 SSD 2 units. I have just replaced with a new OEM battery. It performs very well, I even think it's quite a workhorse till today compared to my 16" Macbook Pro with all Maxed out specs. I don't feel like I've missing anything except that I still use this older Macbook pro in High Sierra for Nvidia Web Driver supports.
There are plenty of 32bit software that is losing support in Catalina or not working in Mojave. That's why I'm keeping this older laptop for other production tools.

Try my suggestion above and see if it works for you.