Cannot do it. Nosirree.
Cannot use a MWBC
As you have stated it in your question, you are describing a multi-wire branch circuit (MWBC).
That is not 2 independent circuits. It is a multi-wire branch circuit.
Further, it has a serious defect in that it is taking power from unrelated points on the panel. Code absolutely requires that MWBCs be both opposite-phased, and handle-tied for common shutoff (which in the real world means common trip most of the time). This defeats your purpose.
Even worse, if you simply put the breakers "wherever" on the panel, then over the years as you rearrange circuits in the panel, you may accidentally wind up with both MWBC legs on the same phase. That means instead of carrying only differential current, neutral would carry the sum of currents causing an overload of the neutral. Neutrals don't have breakers. On almost every panel type, handle-ties force the breakers onto opposite poles, so use of handle ties averts this danger. (Usually; looking at you GE).
So your MWBC absolutely requires either a 2-pole or handle-tied breakers. 2-poles definitely have common trip, and handle-tied breakers usually have common trip (not guaranteed but very likely from handle motion).
For the circuits to be independent, they need to each have their own neutral wires. But wait.
Cannot put 2 independent circuits on the same yoke
That receptacle there, with 2 sockets, is on what's called a "Yoke". That means a single device of any kind - switch, pilot light, GFCI, whatever, that mounts through the usual mounting screws.
So, suppose you run a second neutral. Now you're splitting the receptacle and having 2 circuits each with its own neutral, one powering each socket. You can't do that either. Or to be more precise, the circuits cannot be independent if you do.
210.7 Multiple Branch Circuits. Where two or more branch circuits supply devices or equipment on the same yoke, a means to simultaneously disconnect the ungrounded conductors supplying those devices shall be provided at the point at which the branch circuits originate.
When 2 separate circuits serve the same yoke, again they must be handle tied, and again this defeats your purpose.
There's a very good reason for the handle-tie requirement. Someone servicing the wiring will typically plug a radio into one of the sockets, and trip off breakers until the radio goes silent. Then turn everything else back on, and go to work on the wiring. Think about it. That procedure will leave one of the sockets "hot", unbeknownst to the maintainer. So again those 2 circuits must be handle-tied.
Why would anyone ever put 2 independent circuits on the same yoke, when the MWBC approach does that better? AFCI/GFCI. They don't make 2-pole AFCIs and 2-pole GFCIs are expensive. Often the only way to provision GFCI/AFCI to such a split recep is to have separate neutrals.
Socket size must exactly match breaker size if there is 1 socket
As manassehkatz noticed, you are speccing a 20A breaker that is feeding exactly one 15A socket. Nope. Breaker size and socket size must exactly match, NEC 210.21(B), so you must use a 20A socket or a 15A breaker.
"But people use 15A sockets on 20A breakers all the time!" Because there is an exception for 15A sockets when 2 or more sockets exist on a circuit, which is the usual situation.
You have no option that will allow you to split a yoke.
and maintain independent trip (in practice). Further, you wouldn't want to anyway, because anyone looking at your setup would think you made a mistake by putting both power supplies on the same yoke. (and they'd be right if you followed Code).
Your only option is to fit a 2-gang junction box so you will have 2 yokes, and run 2 independent circuits with either dual /2 cable or /2/2 cable. (can't use /4 cable since you can't re-mark blue to be neutral). At that point you'll have 2 sockets per circuit and 15A duplex receps are fine. If you really want 1 socket per circuit you can get 20A simplex receps, but their rarity means cost.