How can an electronics lab workbench be made feline-compatible?
Without a detailed schematic and system testing of your new cat, it's impossible to say with any confidence.  You'll know from past experience that cats have personalities.  You might find that it just decides to never go into that room.  Or it might live on top of your warm PSU.

And those personalities evolve over time, and also depend on your behaviour towards the cat. Remember that you're talking of typically around 15 years of a love /hate relationship.  Keep kicking it and it'll stay away.  Keep loving it and it'll come for strokes and cuddles on the work bench.

I can only relay what happens with my cat.  He has free reign everywhere and often gets on the work bench.  My issue isn't static discharge, although you can light him up if the weather is just right.  My issue is the play.  He'll sit on things, clamber over things and swat anything shiny onto the ground.  So all loose passive components, screws and small tools gravitate towards the floor.  I loose 5% of my inventory as it's dispersed across the room, down cracks and into the bin.  His worst deed so far has been hiding a small clip from a £30 connector that rendered it useless.  I gave him a proper beating for that.  He also likes to bite through thin wires.  Stuff around 7/0.2mm stranded is the favourite, although he also likes thicker flavours. I have some Sennheiser head phones where you can see the copper conductors through the insulation /shielding. Cable impedance has probably been ruined.

Actually the soldering iron is the least worrisome problem.  Cat's aren't stupid (well yes they are), but they'll never burn themselves on a hot iron as they can sense it.

Electricity is the important issue here.  The cat can't sense it or see it.  The very nature of an electronics work bench means you have electrically hot kit laid out.  Clearly you don't insulate it when you're developing /testing equipment so you rely on laying it out safely on the bench.  I do some valve work at 300VDC which will straighten out any cat's whiskers.

On serious working or testing days, I have no recourse but to close the door on him.  I would suggest that you either get a door, cat type screen saver, or a gold fish.  Just keep it in another room as electricity and water do mix.

Tip regarding bins: Never have an open bin vertically below the edge of the work bench.  The cat will swat things off the bench into the bin and before you've missed it, you've emptied the bin and one of your £150 hand matched Electro-Harmonix valves has gone.  You see they're vole sized and shiney.