The general ROOST design seems to have assumed an inflatable heat-shield. Note however that 'inflatable' heat-shield is a complex layered structure that still needs to survive hundreds of degrees and quite high physical loads. ROOST is listed as 600 tonnes empty so even doing shuttle style re-entry at 3G there is still 1800 Tonnes to be handled by the structure. Think less 'balloon' and more 'bullet proof vest that can inflate'.
In terms of a balloon to land after re-entry, the rule of thumb is 1 cubic meter per kg of lift needed, so 600 tonnes would need something 100 meters across, pushing from 'slightly inflated tank' and into some sort of unique structure all of it's own needing to be very light weight but also capable of handling deployment and inflation into the high velocity air stream. This is certainly possible but not particularly aligned to a conventional rocket propellant tank.
And additional complication is that most flexible materials do not handle the single digit kelvin temperatures of liquid hydrogen, and while 'warmer' at 90 kelvin a whole range of things are excitingly chemically reactive with liquid oxygen.
This probably prevents fuel tank structures for anything launching from earth being re-used this way. More possible would be a vehicle assembled in orbit using large flexible bladders to store liquid propellant or consumables for low(ish) thrust departure and then as empty high drag structures to assist with aerocapture at Mars, but this is a rather different profile than the Roost launcher.
Note that expendable Single Stage to Orbit is questionable, a design claiming both SSTO and re-usability generally involves an incorrect assumption somewhere in the design.