I would argue that offering more equity to EBRD is of no...

I would argue that offering more equity to EBRD is of no interest to anyone (except EBRD itself). The shareholders would be dilluted, Geomet would have to deal with another big player (in addition to CEZ). I think there was some past partnership between CEZ and EBRD for financing the energy company's activities in Eastern Europe but IMHO CEZ doesn't really need EBRD for anything.

CEZ is a large corporation that knows how to do financing, just look at their bonds in the past years:
https://www.cez.cz/en/investors/bonds/issued-bonds
750M of bonds in 2019 with 0.875 % coupon in euros.
600M of bonds in 2022 with 2.375% coupon in euros.

Of course EMH is not CEZ but CEZ as the majority owner could offer at the very least advice, even better guarantee or a structure that would make EMH financing more attractive.

I think the sentence "EBRD financing will be through equity rather than loans" does not refer to any future secret plans but the existing shares which are already known, she just writes in the future tense.