BEBOP

Here's a Transit Of Interest: BEBOP-1. The weebs who named this project were looking at "Binaries Escorted By Orbiting Planets". They used the TESS so, on that serial, it's TOI-1338.

So: the point to it all. The main star 1301 lightyears away is 1.13 M_⊙ F8, so hot; a 0.31 M_⊙ dwarf tightly orbits that. Back in 2020, TESS found a transit at 95.2 days. Given the total mass of the inner stars, Kepler suggests 0.4607 AU. BEBOP did not find a mass for the transit; the radial-velocity aberration fell below parameters. (NASA is dumb.) Planet was too light, and not dense enough. The BEBOP crew set out to constrain the mass. Well... they've constrained it to very light indeed, because they still ain't found it. In a binary system, the red dwarf drowns out a lot of fluctuation.

But they did find some regular fluctuations - at 215.5 ± 3.3 days (they could probably refine this). Also although the radial velocity is only good for msini, here 0.217 Jupiters; much more than that, given the constraints on the inner planet's (low) mass, allow BEBOP to peg a range around the outer planet just for dynamical-stability. That's 65.2 ± 11.8 M_⊕ so, Saturn range. I don't know if this signature means they need to adjust the claimed Marslike eccentricity 0.09 for the inner one. (Probably not.)

So that's one planet with a radius but only a maximum mass, and another planet with a mass-range and, anyone's guess to its radius. Some minima and maxima might be considered; and if the inner planet is fluffy then the outer one should be considered a Saturnlike. One should think.

The BEBOP crew do think that the JWST might be good for this system. Specifically the inner one.

As to potential worldbuilders: Fitzmaurice has reported that a 2:1 resonance is unstable. The moon Ganymede might dispute that; but then, we haven't found any other planets in this system yet. A third planet - if not the 3 in 4:3:2 - might be the 1 in 4:2:1 outside both so in the habitable-zone. So I'm reserving judgement on BEBOP's longwinded look at this system's history. Early system-histories are notoriously chaotic and violent.

Future of the system: if Io is guide, the inner red-dwarf is raising tides and spiraling closer to the F8 main-sequence. I don't give it even to the end of the F8's life. Adding that mass to the F8 will speed up the F8's own time of death. The two planets will be further away than they are now; but not far enough away, so this red-giant is going to swallow both.