"Leaking into the bowl" is often caused by the "SilentValve" rubber disc, which has worn or collected dirt. Replacing the valve is usually a 5 minute job unless, as in my case, you have a Portuguese-manufactured "Oliver" cistern built into the wall. Annoyingly, the first European stockist I emailed in Holland failed to respond. Even more annoyingly, the other stockist turned out to be in Cheshire, just 10 miles from where I used to live!
Of course they couldn't/wouldn't supply the tiny rubber disc by itself; I had to order the entire float valve unit, which wasn't cheap. Nor was the postage and the unit got broken on the way so I ended up replacing only the rubber disc.
Access was via a slot in the wall so it's lucky that I have "girlie" hands and that my arthritis is only mild.
When the valve in the second toilet started to leak, I ordered the kit then called in a Greek plumber. He was totally clueless so I had to stand over him and give instructions.
Oh, and I discovered, later, that the REAL cause of the problem was low water pressure! When the pressure drops below 1 bar, a tired valve doesn't work properly. I had to replace the pressure regulator alongside the meter.