Schumer's statement isn't really about making up some new procedure. He's telling his fellow Democratic senators that Republicans are going to try to stall this thing out in hopes it goes beyond July (when Breyer retires), maybe later, and maybe never happens. McConnell was famous for that stuff as minority leader during Obama/Biden. Schumer is saying the plan is to have the new judge in by July 1st (roughly -- Breyer is retiring at the end of the session, which goes through June), confirmations already take a long time, and if a Republican senator asks you "hey, I might vote for your gal if you add this step that takes a week or two", tell them no -- it's a trick that Democrats fell for for 8 years, and we're not getting fooled anymore.
Here's an MSNBC summary of a McConnell radio interview about how he kept Merrick Garland from getting on the court, allowing Trump to appoint Gorsuch, and his plans to repeat it:
McConnell told radio host Hugh Hewitt last
year that he regards that obstruction as “the single most
consequential thing I’ve done in my time as majority leader of the
Senate.” And he suggested that he’d do the same for any potential
vacant seat in 2024 if the GOP were to reclaim the majority after the
Schumer is saying that talk about waiting to start until the actual retirement (at the end of June), or Susan Collin's statement Thursday that the Amy Coney Barrett confirmation was so fast that we need to slow this one down, or McConnell's suggestion Wednesday that we need to negotiate for a mainstream appointee... he's saying all of that is bad-faith stalling. In the Senate you're not allowed to say anything even remotely disrespectful about another senator. I read "with all deliberate speed" as senate-speak for "with ACB you set the rules for a fast hearing by completely ignoring the other party -- that's what we're doing".
As far as pre-confirming for future vacancies, the next President would ignore it. The President selects nominees and Congress can't tell her how to do her job. That's basic separation of powers. However the pre-confirmation bill was worded, that's what it would come down to. It would be easier to just expand the court, and currently no one wants to do even that.