I’d like to enter Russia through Ivangorod border crossing.
Since I will be staying in the Schengen area for some time as a tourist, how likely is it that the Russian border officer may refuse to allow me to enter Russia?
Knowing that I hold a non-EU passport (Saudi Arabian passport) with a Russian e-visa.
Yes, the Narva-Ivangorod border checkpoint is one of those designated for e-Visa holders (source: https://en.wikipedia.org/wiki/Visa_policy_of_Russia).
The fact that you'll be entering from the EU / Schengen Area is not a problem. Russia's borders with EU countries are officially open and anyone with a valid visa (or a visa-exempt passport) is admitted. However, if you plan to return back to the Schengen Area, make sure your Schengen visa allows multiple entries.
As always in case of Russia, it's advisable to reserve plenty of time for the border formalities. Russian officials can subject you to a lot of scrutiny, either with genuine intentions, or in an attempt to extort a bribe (don't do that!), or a with combination of both.
Finally, make sure not to overstay in Russia, not even by a few seconds, because Russian laws are notoriously harsh about this. Unlike in many other countries, in Russia it's not possible to simply pay a fine on the spot and board your chosen flight (or otherwise leave the country).
As a Saudi Arabian citizen, you are eligible for an e-visa for Russia. Therefore, it is unlikely that the Russian border officer will refuse to allow you to enter Russia if you have a valid e-visa and meet all the other requirements.
Just a heads-up, when are you going there? The Ivangorod border will be closed to cars in February 2024 for reconstruction works. However, pedestrians will not be affected by this closure. You can still enter Russia through other checkpoints across the state border of the Russian Federation. (source: https://www.schengenvisainfo.com/news/russia-to-temporarily-close-ivangorod-border-crossing-to-estonia-in-february-2024)
