Are these engines sensitive to oil choice

[Bonefishblues]

Because such recommendation was made well over 20 years ago when synthetic oil was seen as deeply exotic and was fiercely expensive, I presume?

[AndyV7o]

^This. Mostly.
As has been said, A3 is the apprpriate spec, A2 is obsolete/dead/non existent now, but as has been said, in older engines don't go too 'new' with the specs, they can do more harm than good, it does depend, some may protect just as well and provide other benefits, it deoends on the engine and which oil it is.
If semi 10w40 is specced originally, then thats fine for the engine.
If you wish to upgrade, going fully synth, be it 10w40, 5w40, 0w40, you want one with few specs/approvals, those being older ones. Examples being Fuchs Titan Supersyn 5w40, Shell Helix Ultra 5w40, Gulf Formula G 5w40, Motul 8100 Xcess 5w40. Youd probably be better with a 5w than a 0w tbh, but they are all pretty much the same when hot (hths values aside, but thats another discussion).
You are always better sticking to big-brand oils rather than fussing too much over grades & synth/semi, unless you religiously change every 5-6k. Budget oils (carlube, triple qx, comma included despite what they or their vendors claim) have budget additives and viscosity improving polymers, which can break down early leaving an oil which is way out of grade, not doing its cleaning duties, low oil pressure, and so-on, to which you are blissfully unaware until you start getting those noises, rattles, smoking, poor starting, then its too late... When new they are ok and meet (only just usually) the required spec, its just that they cant maintain it for a long time, unlike the premium oils, which can (and tend to exceed specs to begin with, giving them a 'head-start').