Can anyone tell me what is required for a GPS to be 'IFR-approved'?
I think one would start by looking up TSO C129 etc. This lays down the requirements for functionality, sat failure announciation, RAIM, etc.
Does that simply mean that it may be used for approved GPS approach procedures? If so, it is a misleading description - navigating above 8/8 cloud in VMC with a 'non-IFR' GPS is surely legal, so why not in IMC outside CAS?
An IFR approved GPS is necessary for flying GPS approaches, but it is not all that is necessary for such an approval. The installation has to comply with
AC20-138A (or the usual paraphrased EASA ripoff of that

if Euro-reg). And you need a POH supplement saying so.
For private enroute flight, the regs (UK/Europe) do not prescribe equipment to be USED. They merely prescribe equipment to be CARRIED. So you can navigate above an overcast with any method you like, legally. (The regs don't even prescribe equipment to be USED for an APPROACH, which is quite funny, but I think that while most people fly an NOB approach using a GPS, most people would actually fly in ILS with an ILS receiver).
It is only in BRNAV airspace (IFR, CAS, FL095 plus) that the aircraft must comply with BRNAV which in the GA context means only an IFR GPS, which then de facto becomes mandatory! (Airliners comply with this by having INS, with multiple sensors like DME/DME or, on the really new ones, GPS). In practice, in Europe, BRNAV means you need an IR to be there in the first place.
So, for enroute IMC flight, or any other enroute flight for that matter, below FL095, OCAS, any old GPS is 100% legal.