I hear that shared-neutral or multi-wire branch circuits (MWBC) can have issues when used with tandem breakers (also called duplex, twin, cheater or double-stuff breakers). Do my breakers have a shared neutral?
Tandem breakers in the photo sharing a neutral is a code violation! But may not have been when installed. A quad or double tandem is the only one that can share a breaker if handle tied as the quad breaker bridges 2 poles.
With your current setup the neutral is not doubled as is common because at least the circuits were split, but they are not handle tied. And this has been code for a while.
My jurisdiction has required handle ties for ~20 years. I think the NEC has only required them for ~8 years so if your home is older there is nothing unsafe with the install with regard to overloading the neutral.
The issue with your configuration is if you turn off the top breaker to work on that circuit and the bottom circuit has a load you can get shocked from the neutral.
So you don’t have a fire hazard as is common with tandems but they don’t meet current code because of the lack of handle ties.
I do not know if there are ties for duplex to turn them into quads I have only done the center pair not the outer pair but I know quads are sold just not sure about a quad 15 with ties.