IC1a is called a "float voltage comparator" in the schematic. IC1b is configured as an oscillator. The device operates from a +5V single supply.
Both sections of the device are operating as comparators, not op amps. Both functions can be achieved (better) with push-pull comparators rather than op amps because, well, comparators are designed to be comparators and low noise op amps are designed to be low noise op amps. Low noise is not required at all for these circuits to function as designed.
You can look for devices on manufacturer websites (TI, LT, Microchip, etc.) or distributor websites (Mouser, Digikey, etc.). Distributor sites are sufficient for most things, but you should look at specific manufacturer sites if you have a very specific application or requirement. Here is a Mouser page filtered to show >5V dual push-pull comparators in DIP-8 and SO-8 packages sorted by price to get you started.
My default comparator in this application would be an MCP6542, which happens to be the cheapest one on that Mouser page. (Note that it has a rail-to-rail input, but does not have a rail-to-rail output. That doesn't matter at all in the circuit.)