Yes and no.

The military internet, which is built on similar principles and protocols, yes. The commercial internet? Ehhh. Not so much.

Most internet interconnects are consolidated into internet exchanges, usually in, or near, datacenters. I live in southern Ontario, pretty much every local ISP routes the majority of their traffic, if not all of it, through TorIX in Toronto. There's a datacenter there, or more accurately several, which are cross connected into or through TorIX. Many of the local ISPs do not have redundancy with another IX or datacenter. One notable exception is Bell Canada, who has a strong, and broad transportation network of their own, which connects to TorIX and the IX in Montreal, among others. They're probably the best set up in their distribution layers from what I can tell.

Most ISPs can suffer the loss of one major upstream network provider loss, but not all of them in the IX. Aka, if the datacenter/IX falls, the entire network goes offline.

Take for example a local third party provider of teksavvy. And to be clear, I'm making a lot of wild speculation about teksavvy here, and reality may be very different, but I'm just using them as an example. Normally, small ISPs like teksavvy do one of two things, they either resell DIA connections (direct internet access), which is basically just buying another providers access from them. Aka, you buy teksavvy, but the line you're connected to is from Bell, your internet and your internet IP is provided by Bell, and you pay teksavvy who pays Bell. You might as well be on Bell, but since teksavvy is buying in bulk, you can usually get service from them cheaper than from Bell. Functionally it's the same, so there's a null sum here. The alternative is that teksavvy gets a wholesale connection to you, where Bell (or another "last mile" ISP) provides the connection from your premise to teksavvy, usually through a local IX, your connection still goes into the datacenter, but rather than go from the bell line, through Bell's gear direct to the internet, it goes from Bell's wholesale line, to teksavvy gear in the datacenter, then gets rerouted through to the internet from there. All within the DC/IX.

The IX crossconnects all providers in the DC, which would be companies like Meta, Google, Netflix, the company formerly known as Twitter, etc, and also to other ISPs, so you can directly connect to your friend down the road on Rogers without having your traffic go further than it has to. The IX is where ISPs, providers, datacenters and all other connections meet. A nearby nuclear blast that destroys the DC/IX in your area, would very likely disrupt all communication for the area served by ISP connections routed through that IX.

In rare cases (I believe Bell is set up this way), the ISP will cross link it's distribution centers, which are usually buildings in your neighborhood with the company's logo, but no customer facing area, to eachother all the way across an area into the next area where the next IX is. So you're functionally connected to two IX locations or more. The providers distribution network isn't as fast as the IX to IX direct fiber routes, which usually have fewer devices to go through, but it would work at very limited capacity.

On the public internet, there is a mesh between IX's, but the location of the IX isn't hidden. Any individual connection to the internet is usually only connected to a single IX. Most of the distribution between you and the IX is not redundant.

Then compare with what I believe would be a typical example of a military "internet" (again, I'm just speculating based on highly redundant data principles, nothing more): each location, like a military base, airfield, government complex, etc. Would be connected to multiple other locations in a mesh. In addition, they would have backup links likely through satellite or microwave relay links. So if all of the locations that a base is connected to go down, they can use satellite as a final option. Imagine nine such sites in a standard 3x3 grid. Each is connected to no less than 3 neighbors, and the central base is connected to all eight of the others. The central base is destroyed (or otherwise has their datacom disabled). All outlying bases still have at least two links to neighbors. Communication continues. Another base is destroyed, say, the north-East location. All nodes can connect to eachother without issue, but the north and east bases are down to one link plus backup. The South-Eastern location goes down. The rest are unaffected except the eastern base which now needs to rely on satellite backup, but they can communicate. Etc.

As you can hopefully see, the bases all have multiple redundant links and unless they are destroyed or otherwise have their datacom disabled, they can remain in communication with the other bases.

With the internet, that's usually how IX's are interconnected, but anything on a single IX, is basically fucked if that IX no longer operates. We're all nodes of an IX. An intelligent adversary would target any known centers of telecommunications, and we've made it easy for them my centralizing all of the communications for a given geography into centralized locations which are conveniently published for anyone to see. There are lists of IX locations on the internet for anyone to stare at, including what ISP companies are connected. With a single well-placed, high yield (not even nuclear) bomb or ICBM, all commercial communication systems can be neutralized for an area of attack. They wouldn't even need to destroy a full city block to accomplish it.

Sure, bombing, say TorIX, wouldn't stop someone in, say, Nova Scotia, from chatting to someone in British Columbia, but pretty much everyone in Southern Ontario would be disconnected in an instant. Unable to tweet about the bomb that just went off in downtown Toronto (I believe the IX there is next to Union station, at 151 Front St).

The reason it's done this way is because of money. It's far cheaper to centralize access to an IX, then connect the IX's together. The alternative is to string fiber between datacenter buildings for different companies at different addresses. Getting fiber between geographically different locations is costly, so the companies at the DC/IX all pay a small portion of the fees, either directly or indirectly, to have each IX connected to the others. That cost is shared and the various providers can have access to a limited number of fiber strands that run between locations. Even a handful (like 5) strands can net about 1Tbps of bandwidth or more depending on how it's used. The planning and deployment of such connections can easily run into the millions of dollars. Sometimes significantly more. Sharing in that cost is a good business move, even if you're "helping" your competition by doing so, because they also are getting a benefit from it.

Taking it back to the OP: the blast observed appears to be in a city, where it is likely an IX would be situated, most likely the one that your shelter is connected to. Cellular won't help since a lot of that infrastructure relies on microwave relays back to a head node, usually on the cities outskirts, which then transfers the data to a high-speed fiber line to.... You guessed it, the IX.

The internet isn't designed to be resilient to war. We will lose all datacom if war breaks out, with certainty.

Military networks, though similar in design, have vastly more redundancy, the likes of which, we, the people, do not, and will likely never, have access to.

A couple of years ago, I was working at a grocery store picking onions orders using a web app. The store had enterprise-class Internet service with a provider that had two power utility feeds from two different electrical substations a couple miles apart, for reliability.

One day, though, our service went down. One of the power substations had exploded. Shortly, thereafter, the increased load on the grid caused the other substation to explode, too. The cascading electrical failure took out the ISP's backup generator.

That didn't even take nuclear war, just a faulty transformer. (ETA: The disaster preparedness lesson is to look for hidden dependencies between your backups.)