Advice Removing Ignition Lock - Speed Twin

They’re probably shear bolts, in that the heads shear off at the right torque on installation to prevent easy removal by thieves.
You’ll have to carefully drill them out. I’d have thought the new ignition switch/lock would come with a new set of bolts, but knowing Triumph you’ll probably have to buy them separately

 

Yes, I’ve just looked on WOT and they are shear bolts. Part number 13
https://www.worldoftriumph.com/part...triumphmc/modelid/611001/block/100098052-0-2/

 

Warranty job? Insurance/dealer?

 

So - you know that system incorporates an immobilizer, right?
Looks like you have the key though, so that's a bonus.
The original 'chipped' key would have to match to the Immobilizer ECU otherwise looking at having to get the replacement key matched at a dealer - the best/easiest way to do this yourself is to use the top (mechanical key lock) half of the switch assembly with the electrical bottom half. There are similar (but smaller) shear bolts that couple the two halves together - I can see that set in your second image above (just inboard of the main mounting bolts)
If you go that route, you don't even have to necessarily remove the main shear bolts, can leave that coupled to the clamp. For those other ones, they are already proud of the flange, so you can just cut some slots in there and remove with a screwdriver.