The cookie consent provision under the ePrivacy Directive doesn't care whether they're first- or third-party. Actually, the way it's been worded, you'd arguably need a consent for (strictly non-"necessary") use of eg local storage, too — afaik this hasn't really come up in regulatory practice or case law, but may be more due to regulators' modest technical expertise or priorities.

A conceptually different matter altogether is consent (possibly) needed under GDPR for various kinds of personal data processing involving the use of cookies (ie not just the placement of cookies as such) and other technologies for tracking, targeting and the like. That's why you see cookie banners with detailed purposes and eg massive lists of vendors (since they can be considered "recipients" of the user's personal data under GDPR). In this context, a valid consent (and the information you have to provide to obtain it) is required (at least) when consent is the only feasible legal basis of the ones available under Art 6 GDPR for the personal data processing activities in question. This is where the national regulators have taken strict stances especially regarding ad targeting and other activities usually involving cross-site tracking, for example, deeming that the only feasible basis for those activities would be consent (ie "opt-in") — instead of, in particular, "legitimate interests" which would enable opt-out-like mechanisms instead. This is the legal context of looking critically at 3rd-party cookies, but unfortunately, for the reasons mentioned above, getting rid of such cookies might still not be enough to avoid the minimal base cookie consent requirement when you use eg analytics... :(

It's pretty ridiculous, I know, and it's a bummer they scrapped the long-planned and -negotiated ePrivacy Regulation which was meant to replace the old ePrivacy Directive and, among other things, update the weird old cookie consent provision.