Russian Agency

Russian Embassy wouldn’t be the way to go because they don’t handle visa applications. If you want to avoid online scams, visit the embassy website and find sources they recommend.

You might also review the agency that Rick Steves recommends for the tour that includes St Petersburg.

https://www.ricksteves.com/tours/scandinavia/st-petersburg-tallinn-helsinki-faq

... Embassy wouldn’t be the way to go because they don’t handle visa applications

...huh?

Individual applicants have the right to apply directly to the Consular Division of the Embassy of the Russian Federation to obtain a visa by making an online prior appointment at the web-site of the Consular Division

But on the whole I agree, visa centers are somewhat more user-friendly...

However, this

...the agency that Rick Steves recommends for their tour.

...looks either hopelessly out of date, or just outright strange to me:

• Why would they recommend applying for a single-entry, when the Embassy pushes for the 3-yr multi?

• Why use some strange third-party provider that would charge you basically double the consular fee?

I'm confused...

Why use some strange third-party provider...

Rick Steves does provide the steps to get a VISA on your own. And, if those steps (as they say) "make your head spin," they also offer the information for using a Third-Party Agency.

From what I see on the Passport VISAs Express site, in addition to the $198 consular fee, they charge a $99 processing fee - more for expedited processing. (My nearest consulate, in San Francisco, closed in 2017 so in-person delivery (cheapest) is not an option - whereas it may be for you, living near D.C.)

So, while I can't explain why anyone else would choose a third-party provider, I can explain why I will ....

Normally, I am a DIY (and solo) traveler. For this trip, I didn't want to tackle Russia on my own. For the same reason that I chose the tour, and given the cost of it, I'm willing to pay $99 for extra help navigating the process and some peace of mind.

In my experience, the visa agency I used, following their embassy’s information, reviewed my application for completeness and advised if anything was omitted or miswritten. This prevented my application from being dismissed by the Consular division meaning I’d have to start over.

I used CIBT many years ago. They said fill out the forms, and send them a pdf. They rejected the pdf and sent me instructions on how to create a new one with very, very precise margin dimensions. They said if it was off one mm it would be rejected by the embassy. Necessary? Probably not, but for $80 (if I remember correctly) I didnt have to worry about anything.

James, is the stench of Moscow metro worse than the one in NYC? When I was in Moscow I did not notice. By the way Moscow metro looks more like palace than metro.

... on the Passport VISAs Express site, in addition to the $198 consular fee, they charge a $99 processing fee - more for expedited processing.

I see - and please don't get me wrong, I'm not dismissing the idea of paying a little extra for some peace of mind.
My problem with that particular site is that the "consular fee" is actually $160, the fee they list includes the $38 processing fee charged by the Visa Center, which, as it is, is already a third party (albeit an authorized one).
In addition, the consulate does not "expedite" processing - actually, they do offer rush processing (for emergencies only), but they don't charge extra for it. So I find the language a bit weasely if not outright misleading.

the consulate does not "expedite" processing

I had interpreted that the "expediting" is on the part of the third party processing, rather than the consulate itself. If that is the case, I'm sure it's not going to make you any happier with an agency.

My problem with that particular site is that the "consular fee" is actually $160, the fee they list includes the $38 processing fee charged by the Visa Center, which, as it is, is already a third party (albeit an authorized one).

Yes, I see the exact same pricing on the Russiable.com site, with the fees broken out as you say:

The cost of a tourist visa at the Russian Visa Center is as follows:
$198: $160 in consular taxes + $38 in administrative fees
$18: letter of invitation
TOTAL: $216 per visa