"I try to avoid Google as much as I can so I've been using the Brave Browser for a while now."
-- I'm curious to know what exactly you're trying to about Google? Is it their browser?, their search engine or both? I ask because you can change the default search engine in the browser to DuckDuckGo or you can just do all your web searching via the Brave web search page. "I'd like suggestions for a robust and reliable browser to replace Brave." My suggestion would be to try a couple from this '18 Must-Try Web Browsers for Linux Users in 2024' list, https://www.tecmint.com/linux-web-browsers/ The 2 most interesting on the list to me is Waterfox and Midori. Waterfox is probably the next closest to Brave with the "private tabs with private search" feature. https://www.waterfox.net/ One thing to maybe consider is that if you don't have to have all the latest & bleeding edge web tech. bells & whistles you might be like a simpler, lightweight and faster but less feature rich browser that just works. Maybe something like Konquerer or Epiphany. HTH, ~mc~
