It’s a symbiotic relationship that advances goals for each, but no, they’re not paid ads, and it’s been debunked over and over again. Some game reviews higher than someone feels it should, and they conclude it only could have been paid off, but it wasn’t. Here are a few things that do happen that influence review scores though:

• Publishers know which outlets review their games well, and they prioritize giving advance copies to those outlets and not others; this is why you’ll see the average score drop by a few points after the game’s official release.
• The person on staff who liked the last game in the series, or other games in the same genre, tends to keep reviewing them, because they enjoy the work more, and that review better serves the overall audience. This can explain why a genre-defying game like Death Stranding reviews in the low 80s, but then the sequel is reviewed by people who tended to appreciate the first game, and the sequel reviews higher.
• Publishers know which version of their game is best, and they’ll send review copies of that version. That means they send the PC version of Cyberpunk 2077 when the console version is broken, and they send the console version when the PC optimization sucks.
• When a game is online-only, publishers like to host on-site, curated review sessions with optimal network conditions in a space where all the reviewers definitely have someone to play with. Review outlets have become skeptical of reviewing games this way, and you’ll more often see “reviews in progress” of games where they want the servers to “settle” first. I was surprised to see MS Flight Simulator 2024 actually held to account over its broken online infrastructure, as you’re correct that, historically, they’re not held accountable, but that’s because of this change that review outlets have made in how they cover games like this.