Devices with embedded networking are more prone to this. A 2020 paper mentions some stats and goes into the reasons why further on.
Smart home IoT devices are often configured with hard-coded DNS servers such as Google public DNS. 98% of smart assistants and 72% of smart TVs use hard-coded Google DNS servers to resolve DNS queries instead of using the default DNS server configured at the home gateway. [...] For instance, the Google Chromecast is hard-coded with Google DNS server addresses to prevent access to geo-locked content [...] Other reasons include preemptively avoiding problems caused by mismanaged DNS servers hosted by ISPs, which leads to users blaming the device for the problems.
If the router supports more advanced networking it can redirect external DNS queries to your Pi-hole so nothing escapes. Or else if it has a firewall, that can usually block "LAN to WAN" DNS from anything except the Pi-hole, though that might upset something, like the Chromecast mentioned there.
I've not seen this behaviour before (may be worth checking with TP-Link). I'd guess it's more likely that there's another DNS server being used, and when Pi-hole was offline the other DNS server was used by virtue of being one that was still responding. A lot of OSs now will contact all configured DNS and go with whichever one is responding the fastest. That's probably Pi-hole while it's up and running, and anything else while Pi-hole is offline.
Some Android phones automatically add an extra Google DNS, which is annoying.
You can get an idea of which DNS services are in use by going to DNS leak test and running the Extended test. If you're seeing various services like Google in there then that's a good indication it is another DNS server. The reference to "leak" is more for VPNs, it's not really a leak in this use-case, but still a handy tool.
Pi-hole itself is very stable and if it's running on a Pi with a decent quality SD card and good (eg official) power supply, in my experience it's been rock solid for years. One risk in that setup is if there is a power failure. You can buy a mini-UPS add-on (eg this one) for the Pi which allows it to stay up for a short while and can shut down cleanly if there's a power cut.
Take periodic backups with Settings > Teleporter so you can restore your settings to a fresh image if something does go wrong.
Handy tip – Real VNC provides a free of charge license to Raspberry Pi users for non-commercial use. You can enable VNC in
raspi-config, create a free account at RealVNC and then sign in to that from the VNC icon on the Pi OS desktop. Now you can use VNC Viewer on any computer anywhere and access your Pi OS desktop. This means you can jump on to a desktop on your home network if needed, and it doesn't need any ports exposing to the Internet.
Edit – just remembered you said you run it on a NUC. Hopefully still useful info for Pi users, and if you can sort a UPS solution for the NUC then the same applies.