I'm afraid there's no single specs that can be used to know what can make a tire comfortable. The main criteria is suppleness (besides pressure, obviously), that allows a tire to easily deform to absorb asperities in the road (provided that the pressure is low enough to allow the derformation), but it's not a "metric" per se. By contrast, a rigid tire will deform less and transmit more energy to the wheel axle, with results in comforting.
About TPI, I understood that it can be used as a red flag, 60TPI is the minimum, less reveals a low quality tire ...but that is not per se a sufficient, as the construction of the tire also plays a role and is not always described in the spec. To give an example, the legendary stiff Schwalbe Marathon Plus has the same number of TPI than the Schwalbe G-One R, a tire that is considered to supple. Terravail also sells tires in two versions: light&supple vs durable, and same number of TPIs for both of them.
Suppleness is usually a feature that is found in performance/premium tires, as supple tires typically have lower rolling resistance. Theoretically, I have the impression there's a correlation between rolling resistance and comfort: one of the factors that causes rolling resistance the energy required to deform the tire. But rolling resistance is rarely mentioned by manufacturers, and if it is, they don't explain how it is measured. But to compare tires of the same maufacturer of the same family it can be a proxy. There is also this website: https://www.bicyclerollingresistance.com/ but it's a lab testing that may not be representative in real situations.
Features like puncture protection layers for example influence rigidity, as well as using a tube. So it's also compromise.
In the segment you mention, I have the impression there are mostly "cheap" or "puncture resistant" tires. The comfort offering exists but is very limited, but is growing. When I did this research last year for tires of this kind of size - for a commuter that should be comfortable on cobblestones, I settled up for the Schwalbe Marathon Almotion (or Efficiency if riding mostly on tarmac). Schwalbe has the "balloon tire" label for largish tires meant to be ridden at low pressure (with tubes) - Big Apple and Big Ben, that are to my knowledge, the only "non performance" supple tires. There might be other tires available in other regions and from other brands, so it's not an endorsement.