How to fully update my outdated Mac with the last available updates?

I have a MBP late 2013 (Intel) running on MacOS 11.7.10 with xcode 13.2. I know Big Sur ( MacOS 11 of 2020) was the last supported OS upgrade. So, since 2021 I have not opened Software update as I was not expecting any update. Now, when I was upgrading an app in HomeBrew using 'brew upgrade', I got an error message: >Your Xcode (13.2) is outdated. >Please update to Xcode 13.2.1 (or delete it). >Xcode can be updated from the App Store. In "App Store" > Updates, I see that Xcode 13.2.1 is ready to download. But on clicking it, I get the message that I can download an older version. But when I click to download the older version, the same box keep re-appearing 3 more times, and it goes away and nothing happens. Then I open "Software update", via Apple logo > About this Mac. Its been "Checking for updates..." for 2 hrs and still on. Nothing is happening. I downloaded "Xcode\_13.2.1.xip" from [https://developer.apple.com](https://developer.apple.com). I was going to install it, that's when I thought I shall ask here. So, I have 3 questions: 1. My software update & app store - is it broken or is this normal for outdated systems? 2. I was under the assumption that Xcode 13.2 was the last version I am going to get. Not sure when 13.2.1 was released. Now, can I check which is the last supported version of xcode for my mac? Are there any other vital components of MacOS like xcode that I have to manually upgrade? 3. What is the software update policy of Apple? If tomorrow they find a huge security flaw, will Apple offer a patch? Will that patch be pushed via "Software Update"? Should I regularly keep checking "Software Update" for an outdated mac?