While, I’m not sure if you’re in the US or elsewhere, here is my response from a US perspective. Another consideration is what carrier do you use, especially if you’re in the US. A phone with a user-replaceable battery that is under $300 is going to be hard to find, at least new.
My recommendation for a new phone would be the CMF Phone 1. While the battery isn’t user-replaceable in the “pop out” sense, it is designed with a more accessible battery for easier replacement than most modern smartphones. https://us.nothing.tech/products/cmf-phone-1
For used, this is also challenging. If you can find a Fairphone 3 or 4 in the US that works with your carrier, that would be perfect. The Fairphones have batteries that are removable by popping off the back cover. They are typically around $300 I think.
Nothing OS is a custom OS by Nothing Technology Limited built on Android. It is not privacy focused like you would get with GrapheneOS but has very little bloat. It is proprietary to Nothing phones. There are unofficial versions of /e/OS available on on XDA for the CMF Phone 1. The Fairphone 4 also has the ability to run custom ROMS like /e/OS and LineageOS.
Here is a video talking about putting /e/OS on the CMF Phone 1: https://youtu.be/TkTzmM9izCo