I recently switched to using a Mac as my main PC and I'm looking for a good app for browsing and playing my local music collection of FLACs and MP3s. Any suggestions?

I think foobar is probably the best option I know of. People use MusicBee a lot these days but it has no Mac support, though there are some guides to get it working on older versions.

macOS should be able to read any Windows-formatted drives, so you can copy and paste (or drag and drop) to get the files from your external drive over to your Mac. iTunes and Apple Music don't play .flac files though, so you may want to use something like foobar2000 (https://www.foobar2000.org/mac) to play them or to convert them to another format that is readable by Mac programs. WAV files are fine, and AIFF/ALAC are both lossless formats that iTunes and Apple Music can read.

I just gave foobar a try but the Mac version doesn't support components which means no Columns UI, and the standard UI is way too basic for my needs (a column browser in particular is what I want). Any other local music browsers / players for Mac?

I'm happy to report there IS a good local music player for Mac. It's called Swinsian and I don't know why it took so long to find it but I'm glad I did. It has a traditional iTunes / MusicBee type layout with playlists on the left and the main library browser to the right. It doesn't have the crazy amount of features and customization as MusicBee but it's much easier to get used to and does have all the essentials: optional column browser, optional album art browser, customizable column order and sorting, smart playlists and tag editing. It comes with a one month free trial and is $25 to purchase, which I did happily after a few days of use.

https://swinsian.com