Okay, I've reviewed your description and the images (though I'm limited by only your description of the images). Here's the situation and what you can likely do.

Understanding the Situation Panel Type

If your panel is indeed an Eaton BR panel, that's good. It simplifies things.

Quadplex Breaker

The existing quadplex breaker is likely a space-saving measure. It combines two double-pole breakers into the space of one. This indicates space constraints are possibly a factor.

Desired Configuration

You want a combination breaker: a double-pole 30A for the dryer and two single-pole 15A breakers, not linked together. This is perfectly reasonable, and your needs are understandable.

The Solution

Yes, what you're looking for does exist, but not in a single unit as a direct replacement. Instead you are going to need multiple breakers.

Here is the best approach


BR230 - Double-Pole 30A Breaker

Purchase a standard Eaton BR230 double-pole 30A breaker. This will be for your clothes dryer.2.

BR115 - Single-Pole 15A Breakers

Purchase

two standard Eaton BR115 single-pole 15A breakers. These will be for your general receptacle and lighting circuits.3. Installation Plan

Remove the existing quadplex breaker. Install the BR230 double-pole breaker in the space where the quadplex breaker was. Install the two BR115 single-pole breakers in adjacent available spaces in your panel. They do

NOT need to be connected together. In fact, they must not be physically connected.

Why a Combo Breaker Doesn't Exist

While it might seem logical that a single unit exists, they are exceptionally rare because they don't provide the flexibility that standard breakers provide. Standard breakers are much cheaper and easier to find.

Important Safety Considerations



Turn Off the Main Breaker



BEFORE doing any electrical work, turn off the main breaker to your panel. Verify it's off with a non-contact voltage tester. Wiring

Make sure to properly connect the wires to the new breakers according to code. The 30A double-pole will need two hots and a neutral. The 15A breakers will need a hot and a neutral.

Grounding

Ensure all grounding is done correctly.

Wire Gauge

Ensure all of your wire gauges are correct for the breaker amperages. A 30-amp breaker will require larger gauge wiring than a 15-amp circuit.

Permits and Inspections

Depending on your location, you might need a permit and inspection for electrical work. Check your local regulations.

Important Notes about the Current Panel



Wire Size

Make certain the existing wiring is correct for the breaker that is currently installed AND the breakers you are about to install.*

Fill

Make certain that your current panel is not filled beyond what is safe. If your panel is already very dense with breakers, you are going to want to reconsider adding more.

Recommendation

If you are not comfortable working with electrical panels,

hire a qualified electrician. Electrical work can be dangerous, and improper wiring can lead to fires or electrocution. Flag for review