Oh my sweet summer child. During the paper voting, only the act of casting the vote happens on paper, the rest (tallying, allocation, voter lists etc) is all electronic. Both in Estonia and elsewhere.
https://media.ccc.de/v/34c3-9247-der_pc-wahl-hack
Granted, that's the benefit of paper votes: You can always count them again.
Each voting station gets a paper voter list. When one votes, their name is struck off this list and added to a new one by different people. Then ballots are tallied one by one in front of observers, and the count and both lists are checked to match.
Finally, the preliminary tally is sent, but physical evidence is brought to a nearby court by the station members for custody, plus a copy of some documents sent by mail, so the electoral boards can aggregate the results during public sessions.
(As Ireland is a PR-STV country, this leads to _extremely long_ vote counts. I think the most recent European Parliament election didn't assign all the seats for about a week.)
Hmmm, maybe I’m underselling this, you probably can cheat by a lot of percentage points still and get away with it. But at some point if the official results are like Putin’s while local results show everyone hates your guts, it might start tipping people off.