It is possible your router supports hair-pinning or (NAT loopback).
When it detects you are trying to access the external IP address (even if it is cg-nat) it is smart enough to router the data basin internally and some are smart enough to apply firewall rules as well...
Hate to say this (being an iPhone user) but the Android apps are way better :-( If you can face using one try https://play.google.com/store/apps/details?id=com.manageengine.wifimonitor
Apple ~~tweaked~~ crippled the API used by the tools on mobiles a few years ago and quality of results dropped dramatically even for home use.
If you have a MacBook try https://www.netspotapp.com and request the free trial (no obligations is their byline) but TBH its worth the entry cost (£144) to allow you to check the results of the changes and redo each time the office moves around :-) The results are way better (i.e. more accurate) than on a mobile app.
You are talking about a manual watchdog timer system. There are low cost and free systems to do things like this - a search for network and application monitors will turn them up.
Its way better to try to address why the core program dies that patch around it this way but as that's not always easy (or cost effective if the code is out of maintenance) then just create a small program that checks if the core app is running and restart it if its not. This can be run from the system scheduler every few minutes.
If you have no way to tell the program has died (other than users shouting) then you could look to send an email to a mailbox that's monitored by a background program and restart when it gets one.
Another way is to create a simple web page that is hosted on a box and use that to trigger the reset.
No matter the way you go (I lean to copper less you fancy trying to use pre-made fibre cables) then make sure:
I've been using ICY BOX on an old 2012 Mac mini for years and would happily use Yottamaster kit for the same task. My third option would be G-Technologies.
Not keen on hardware RAID built into enclosures but I've had raid controllers AND software RAID fail on me before today.
Just noticed it's a TalkTalk router (and then felt sorry for the OP).
Their forum says the error is the router cannot log in to the network. Could be fried or an account problem (if not a general network outage). If the reset has deleted the account details they may need TT to help with the settings / password in any case.
Will stick to my original point and with them luck!
Any reason you have not called your ISPs help desk?
IIRC Getting the LetsEncrypt certificate for NGINX Reverse Proxy requires direct access to the web site on port 80 - you are behind CGNAT and stuffed...
Possibly have a look at Cloudflare tunnel (Cloudflared in Docker) - this gives you http / https access with certificates. I used these instructions and it took less than an hour to get up and running https://www.crosstalksolutions.com/cloudflare-tunnel-easy-setup/ Note my TTL on the domain was set low to speed up transfer of name servers.
This also lets me access the sites directly using the full DNS entry even though my router does not handle hair pinning - no need for a local DNS server anymore.
Note the above are slightly out of date to the screen layout but in principal they work fine.
There is a small security concern - Cloudflare can intercept all traffic (even to/from https sites) internally - that does not worry me but your use case (or principals) may differ :-)
Do you really need an SSD if there is only you watching things?
I can happily stream off a single NAS HDD to three users without straining things!
I've stopped using my wiki as I discovered https://www.bookstackapp.com/
The advantage is it forced me to organise my notes rather then the mess I had before while still maintaining the ability to link between scribblings...
Simultaneous charge and supply circuits cost a fair bit to design and implement.
It's a lot cheaper and profitable to build a basic 'brick' that can be sold to hundreds of thousands of 'phone users rather than a premium product for a few computer folk.