Hakko FX888DX-010BY - Digital Soldering Station with Rotary Encoder (Blue/Yellow Housing)

That Milwaukee you have is mostly likely meant for plumbing and electrical work not electronics so yea you should get something else. Pinecil is a decent mid-tier iron with a beginner friendly price. https://www.amazon.com/PINECIL-Smart-Mini-Portable-Soldering/dp/B096X6SG13 If you want something higher end there is always the various Hakko models. https://www.amazon.com/dp/B0D4DJW54S/ I have heard this one is pretty good.

I would stop trying random pencils unless you can confirm pinout and heater resistance. The Hakko FX888DX makes more sense as a full station replacement.