Are you able to measure the input current during a weld?

I suspect you might not have enough copper in the secondary. Fully insulated wires take up a lot of space; there’s a reason magnet wire is commonly used. Several parallel turns of e.g. 6mm^2 magnet wire would be preferable.

Your SSR generally should be in the phase, not the neutral.

If you have a 230V supply and a 230V transformer, you are fine. I believe they thought you were using a 120V supply on a 230V transformer.

Raising the input voltage will probably not get you what you want.

TO220 package diodes are pretty common in SMPS applications, so I’m not sure that’s a guarantee.

EDIT: Not sure what you’re getting at here? Royer doesn’t seem to need anything other than a rectifier on the secondary, and plenty of topologies use two power transistors on the primary.

The second smaller transformer below the main one does tend to suggest it could be a Royer, at least from my reading. I don’t see the extra switches needed for it to be a PFC stage.

There’s still a little SO-8 and optocouplers.

That’s not a mains frequency transformer. Not enough steel. It’s a high-frequency all-switchmode supply.

However, that’s not to say you can simply adjust the feedback and have it safely deliver near twice the voltage. The secondary side diodes and capacitors probably won’t be up to it, or will have a very limited life.

The transformer does have a ratio, and the marking makes it clear that this is a specific part for the 12V model. How much leeway there is will depend on topology. Flyback are generally fairly flexible. Other types less so.

Starting with a 24V model and either adjusting the feedback resistors or adding a few diodes would be near trivial. Many will already have a potentiometer that provides that degree of adjustment. Starting with a 12V model is an uphill battle.

In many cases, the primary power consumer on an Arduino is the power LED. Remove it.

Buck converters are more efficient at high loads, but sometimes have higher standing/quiescent losses. You’ll need to select carefully.

At reduced clock speeds, most ATMega parts can operate from 2.7 to 5.5V. Depending on what other parts you have, you may be able to operate directly from a 1S lithium cell with no converter or LDO. You’ll still need a battery protection chip/PCB to prevent over discharge.

The other thing you want to do is put the micro to sleep for as long as possible.

Three in series per 300 ohm resistor would be OK with those.

Do you have a datasheet/part number for the LEDs, or at least a picture and diameter?

Because battery voltage reduces over time, the LEDs will get dimmer as the battery drains fairly quickly. If possible, running it off a mains plugpack (e.g.12V like for a router or external hard drive) would be good.

An example UV LED has a forward voltage of nominally 3.7V. Two in series on a 12 (8x1.5V) supply gives us 12V-(2x3.7V) =4.6V to drop across the resistor. We want ~15mA, so need a very roughly (V/I =R) 4.6V/0.015A=300 ohm resistor.

When the battery is nearly discharged, at 1.1V/cell it will be 8.8V, giving 1.4V across the resistor and V/R=I 1.4V/300ohm= 4.7mA.

So you would connect each pair of LEDs as:

BAT+ RES +LED- +LED- -BAT all in series. Like this.

You’ll need another 10 300 ohm resistors for 15 total, one per pair of LEDs.