Some will, the display backlight needs power after all and a fair amount. I believe most displays have either an internal battery, maybe some can draw power from the laptop. The former will have negligible impact on battery as the computer only needs to render the image for the second screen and send the video output the display, the latter will have a big impact on battery as on top of all that, had to power a big bright backlight.
For power efficiency, you get the added benefit of being able to run on battery backups for longer. This for pihole, file servers, etc. can be a lifesaver
To add, open source projects tend to give YOU more control over the data (if not the mainline version, some fork will probably exist. Its far more profitable to target a big company for a ransom than an average Joe. Obviously, as long as you don’t fall for one of the classic blunders.
for sure a proxmox server is great, id just say don’t go for the cluster just yet. Frankly, most self hosted stuff is dockerized and thats a huge plus. And it seems you already have that sorted out (id even ask you if casa OSs fileshare and an external drive could handle the NAS aspect).
I say this not to be a killjoy, but because I have a proxmox node I both overbuilt (for small services and running off a UPS) and underbuilt (for multiple big VMs) all because bought it to, and i kid you mot, “use it for NAS, and a window VM and run other random things that I don’t know yet”. 2 years in and i still don’t know what those random things are.
So, my two cents: start cheap get a node to learn and understand where you want to go from there.
Doesn’t work well for thicker beverages like milkshakes or iced coffee’s. But for most drinks i agree no straw is best.