It's voting for the candidate most likely to win against the main party's candidates. The app's purpose is to concentrate protest voters on one candidate without spreading them over all of them.
They are rigged, but not as fully as they were in e.g. Belarus.
Russia is a giant country with 85 "states" and around ~100k polling stations, so the process is very complex and involves different voting and administrative cultures. In some of those states they are fully rigged, with 95% turnout and 98% votes for the ruling party, but in some the elections are surprisingly fair. In a lot of others they can be made fair if any poll watchers are present. Overall the thinking is that they add themselves 10-15% additional votes across the country by straight up voter fraud.
The main way they rig the elections right now is by not allowing anyone who could win to participate and then throwing all of the state resources towards promoting their candidate. That's why consolidated voting for a single opposition candidate can work in this context.
To add to this: this elections are run independently in every region. The government's ability to rig them in one area does not affect the outcome in another.
Yes there is a lot of evidence. From blatent ballot stuffing to more tricks like changing names. This time they even shaved someones head to make them look like the candidate ;)
A concerning development this year is they allow online voting? Which seems like the easiest way for them to flip just enough votes to win, without giving themselves 95% of the votes.
Sometimes they are, but (mostly in large cities) people sign up as election monitors to prevent it. Sadly, most of 90 000 polling stations are not monitored by independent observers.
The main way to control elections now is not letting opposition candidates to get into the ballot. For example, on this elections many candidates were rejected because they are "linked" to Navalny's organisation that was admitted as an extremist organization by the court. Some people are rejected because the signatures they have collected are deemed invalid. Obviously you cannot win if you cannot get into the ballot.
There also is electronic voting (voting over Internet) which is difficult to monitor. It is also worth noting that while you can vote over Internet, you cannot collect more than 50% of required signatures for being added to a ballot this way.
Given an address, the app provides the name of the suggested candidate in the corresponding voting district. The idea is to consolidate votes around only one candidate who does not belong to Putin's party.
In Russia, many potentially popular candidates are not allowed to run, were imprisoned, or otherwise persecuted, and in some cases killed. Those who remained are often spoilers or people you would not willfully vote for. So usually, people unhappy with the regime either did not show up for the election or spread their votes between many unpopular candidates. That is how Putin's party has support from 20-25% of the population according to various polls but commands 75% of the seats in the parliament. This, and election being rigged. So, the idea is to consolidate the votes of the people who are not happy with Putin's regime. If anything, just to send the message. And that's "protest voting".
The list of the candidates to support was published at the last moment to avoid the risk that they will be removed from the election. The app is the main channel to publish this list because it can auto-update and bypass Internet censorship. Normal websites are often inaccessible without a VPN. Google and Apple shut off this channel.
It is a simple list of candidates recommended to vote for that, according to Navalny team's research, have the highest chance of defeating the Putin's candidates.
The idea is that instead of spreading votes and allowing the baddies to get the highest percentage (but not even close to 50%) and win, people would concentrate their votes.
If you are still in disbelief, that Kremlin would apply such an enormous pressure just to ban a simple list of voting recommendations, I want to remind you that this is exactly what happened last night: the recommendations were posted on Google Docs and Russia decided to ban the whole Google Docs service for that.
