Intel 11th Gen i7 laptop as server?

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Any general advice on how best to utilize the laptop?

Oh yeah, you'll be much happier with the performance. I would recommend grabbing either a laptop stand with an open bottom or, probably a better bet, some sort of cooling apparatus. These would definitely extend the lifetime of the laptop. Last resort would be to run it upside-down so the fans have ample airflow.

Is there a major advantage to running Ubuntu (which I have never used) on it versus Windows?

I have strong feelings about Windows + server in the same sentence. However, I would ask whether you're looking for a project or looking to get set up ASAP? If the former, try Ubuntu server (it's CLI-only). Even Ubuntu Desktop has a way smaller footprint than Windows. If the latter, just use Windows. Advantages to Ubuntu? Ease of access (SSH from another machine, run multiple sessions simultaneously), super simple virtualization via Docker, very low overhead compared to Windows, community support, well-established and fixed fairly quickly, crazy extensible, probably the easiest version of Linux to learn. There are a lot more.

A big one I found recently is that you can get Ubuntu Pro for free. Running on a server this means faster CVE patching for longer, automated updates, additional updates, fewer required restarts, extra protection and hardening if you wish, and more. It has been a blessing for my server.

Any issues with running the server on the laptop with all the media connected to a NAS?

Nope. You may run into permissions issues, but that's with any kind of remote storage setup. You'll just have to troubleshoot a bit. We can likely help.

Other than keeping it properly cooled and removing the laptop battery to avoid lithium ion sadness, are there hardware tips?  Thanks!

Whoops, obviously started this before reading everything. Make sure it's hard-wired; buy an ethernet adapter if it doesn't have (a functional) one. If you can open the case, canned air the shit out of it prior to starting use as a server. Remove or disable everything you don't need (hardware AND software). Otherwise? Just do it. I'm sure it'll be fun.