There has been an oversupply of transformer manufacturing plants in the world for decades. No one needs the Internet to start building more. The designs already exist and most of the small manufacturers are still using manual or at most semi-automatic winding machines. For large transformers this is true even in the big manufacturers like ABB and Hitachi. Stacking the cores can easily be done by hand.

The bottleneck would most likely be the supply of core steel. Increasing demands for efficiency have pushed core steel manufacturing into a few high tech manufacturers.

Other things you haven't considered:

Fuel pumps run on electricity, so you need to get them working before you can get any materials, everywhere, or you won't be able to fuel all the ships and trucks necessary to move anything.

Phone lines (and the internet) runs on electricity so you need to get them back up to coordinate everything.

While you are trying to rebuild your transformers most of the food we have in storage will rot. Think you can fix the grid fast enough to prevent all your factory workers leaving to forage?

It's incredibly naive to imagine that this is an easy problem to solve. The amount of stuff that you have subconsciously assumed to make this scenario work is staggering.

Yes... so priority will be to find diesel generators to get refineries back online. Individual pump stations will, if needed, scavenge solar panels or generators to get their own pumps up and running.

Governments will prioritize food and electrical infrastructure, likely banning transport of anything not critical to these two categories. Trucks traveling to transformer plants (and plants converted into switchgear plants) will carry food to the plant if necessary.

I'm not trying to paint a rosy picture... that everything will be OK everywhere. Some areas will manage better than others. Some areas may well turn into riot zones as people fight each other for food. Recovery will initially be spotty and uneven.

But I'm 100% confident it will not be a semi-permanent collapse of civilization. I'm also 100% confident some metro areas (and the farming areas nearest to them) will be back up and operational within 1-2 weeks up to 1-2 months depending on local circumstances.

Like I said: it wouldn't be a pretty situation but people aren't just going to sit back and accept the destruction of civilization and/or death. People will dig out old textbooks on electricity and figure it out.

Transformers are simple devices. The first electrical gear was a janky DIY affair by modern standards. We wouldn't wait 10 years to manufacture modern switchgear... we'd cobble together literally anything to bootstrap electrical power. It would start off as isolated islands with nearby generating capacity and where enough gear was still operating then spread from there. Major cities would be back online first, followed relatively quickly by medium cities. That might mean that only certain parts of those cities have power initially with neighbors having to share fridges as only every other block is repaired.

Small cities, towns, and rural areas would be proper fucked for a while... possibly a year or more. But before a year was up enough power would be restored to manufacturing that many of those people would install solar grid-forming and/or battery systems.

For whatever it is worth we are better positioned now than in the past. More and more people have distributed generating capacity with solar PV and grid-forming systems like Enphase IQ8 can form a microgrid just from solar energy without a battery (at reduced capacity depending on sunlight conditions). Even 10-15 years ago solar was useless without a grid to tie into so a full grid outage would be close to a 100% outage. 10% remaining may not be a large amount but its a lot more than 0 and enough to move your neighbor's fridge/freezer into your garage and keep food cold for the whole neighborhood.

(Disaster resilience is a feature of distributed solar PV, especially with batteries, that is almost never talked about)