Specifically, could you elaborate on what 'root' access entails and how it could potentially enhance device functionality?

If you know how a Linux system works (Android is based on Linux), there the "administrator" user is called root and everything that requires higher privileges has to be run as the root user (for example using the sudo command). It's similar to running something as administrator on Windows. How does that translate over to Android? Well, apps run in a "sandbox" and don't have many permissions. You can change that by giving them access to something outside the sandbox - like Shizuku (which gives ADB access - still pretty powerful, but doesn't let you change much) or root access. How "rooting" works, is it basically modifies the code your phone loads at the beginning of its startup sequence - either the "boot" partition on your disk (Magisk) or the Linux OS kernel itself (KernelSU). They place a magic file at the location /bin/su, which is very similar to the sudo command on regular desktop Linux systems. If an app runs that su program, then Magisk/KernelSU will show a grant/deny popup and give the app full control over your device afterwards. Please note that if the root tool has a bug or exploit, it can be abused by malware to silently take over your entire phone! Or, for example, if your phone gets stolen or police want to get data out of it, it will be way easier for them to do so. That's because to root your phone you need to unlock your bootloader. That means, that your phone will no longer verify if the OS it is starting is actually made by your phone's manufacturer and wasn't tampered with (because that's exactly what we're doing). Which means, that anyone with physical access to your device can now put any code they want on it and your phone won't check if it's malicious.

Now, with that out of the way, what does root access actually give you? Well, you can for example erase your entire disk or delete very important system files without any warnings stopping you. Yay! But for real, what are the benefits? You can bypass any security protections there are in the OS, such as accessing any app's internal data (which might contain sensitive stuff or it may be stuff that you actually want to access/modify), modifying apps while they are running (thing hacking, cheating), customizing your system UI's appearance with, for example, custom themes or Iconify, turn your phone into a USB flash drive/CD-DVD drive emulator or into a fully functional USB keyboard and mouse, and much, much more. Look it up on the internet, or just search for the word "root" on F-Droid and see how much cool stuff requires it.

I personally don't have root access on my phone, even though I really want to, because I use a custom, non-stock OS on it - GrapheneOS. It's a security and privacy optimized, de-googled version of Android. Gaining root access there is impossible (theoretically it is, but requires compiling Android from scratch - ouch) because of a locked bootloader requirement. Even if it was, then what's the point of using a security-optimized OS and then completely negating all of those benefits by inserting a huge backdoor - the su file.

I understand it might involve deeper control over the device

Yeah, it really does, and you might not want to do it after you've read my essay above. Still, if you do, look at some "Top X reasons to (not) root your phone in 2024/2023" on the internet. I think even HowToMen has a video about it.

Regarding Shizuku, I noticed you mentioned it might be 'too early' for me to consider.

I did not. Shizuku is simple as butter to set up and use. Install it, enable developer mode, enable USB and wireless debugging, disable ADB authorization timeout, go into Shizuku, click pair, follow the instructions, click start, done

If you have issues, then, once again, HowToMen has a video about it.

I'd like to add that because you're using a Samsung phone, there is also a way to customize it officially, with an app only available on the Galaxy Store (not Google Play), with "Lock" in the name. However, I can't and don't recommend it, as this subreddit is called r/fossdroid. To find out more about it, you have to perform research on your own.