Then I looked at the cap and realised it has this wedgy shape slightly protruding.
Well, hold the jar strongly in one hand and hit that part hard with the ball of the hand near the base of the thumb. This deforms the cap just enough that air gets in.
Might take a couple of tries to get the hang of it but has worked for me ever since: I've never used the spoon trick again since at least a decade.
https://avantihomewares.com/jar-opener-blue/
I've got one in my kitchen drawer, and it works well. Occasionally you get a jar where the gap between the lid and the jar is too narrow for the tool to slot in, but that's rare.
Tap the edge of the lid on a hard surface while pointing the jar 45 deg downward.
Tapping the lid is a common suggestion, but the magic ingredient is the downward angle.
* by found I mean shown, by a senior professor of mechanical engineering.