I wouod like a power cord recomendation that's in the budget category

VH Audio Chris Venhaus will build a cable for you and your spec the parts wire connectors etc. He built me a couple cords a little above your price range that I love. And he's a pleasure to deal with.

https://www.vhaudio.com/

Was going to mention VH Audio as well, but I was going to suggest buy the plugs and cable from Chris and build your own. I’m sure Chris will give you your best option either way.

I've tested a lot of different power cables over the years. And something that often surprises me is the fact that, when I change signal cables, for example, the sound "changes", while when changing power cables it is often very obviously "worse" or "better".

With a limited budget, I can really recommend Wireworld's cables. From the cheapest entry model and up. I have always thought that they provide a positive and steady improvement overall. Their copper cables are preferred, while the silver models require caution and testing ..

I’ve been very happy with Cullen 

I’d go with Cullen too, although I recently heard about Audio Envy that also sounds very intriguing.  Most of these guys offer a return period so you can give one a shot with very little risk.  Given the quality of your preamp I’d recommend you at least try a better power cable as it could potentially make a big difference for relatively little extra cost.  Best of luck.