Moving gmail messages to folders via the mail application - still showing in inbox

Hello,

I have a gmail account that I use for business. I'm attempting to use the native mail app on my MacBook Air to sort and view my emails from that account (and other non-business accounts). I would like to be able to sort my emails into separate folders based on the subject. I have created the folders I want, and have moved the emails into them. I can verify that the emails all appear in their corresponding folders as expected (post move). However, they are also still visible in the inbox. This is super frustrating. I like a clean inbox. I want to go in there, see what's new, get rid of the garbage, and place anything I need to keep in its corresponding folder, but what I get is just a mess of every email I have never deleted.

I've seen a couple other explanations indicating that this is a function of GMAIL specifically (adds tags to to emails - not real folders), and that it's expected. This can't be the final answer. If there are tags added, then the mail app should be able to sort the tags into their respective folders such that the emails don't show up in both the folder AND the inbox. Perhaps a setting somewhere that I need to adjust? If you haven't already guessed, I'm rather new to Mac, but I'm learning fast. Appreciate any info you can share about this specific issues. Thanks!