A treaty under international law can be any of the following in US law (in roughly descending order of the force of the agreement in domestic law):
1. A treaty.
2. A “Congressional-executive agreement” under which the executive makes an agreement supported by statutory authority, or
3. A “sole executive agreement” under which the executive makes an agreement, and then seeks to apply it through statutory and other executive authority even though the agreement itself is not specifically authorized.
IIRC, the legal theory of the Obama Administration was that Paris was within the scope of authorized international agreements under the Clean Air Act and/or other environmental laws, and thus they treated it as a Congressional-Executive Agreement; as such, the underlying statutory authority remaining in place, Biden would as free to rejoin without Senate ratification or additional Congressional action as Obama was to join in the first place.
The US just needs to:
* make a plan (doesn't need to make sense or work or have details),
* measure some things (you define what you measure so again, pretty easy).
* the accord prevents anyone critising or questioning your plan or measurements. So it's 100% mark your own work and I won't check.
It's nice that Biden has put the US back in, but he can do so exactly because it won't make any difference to anyone's lives.
And that's the real problem. The world needed a binding climate agreement and it needed it in 2000. Here we are 21 years later and we still can't manage a non binding, "you do you", placeholder...
