Also solar panel manufacturing is a very intense process with a lot of carbon impact

The carbon impact mostly is energy used in production. So it's high when you produce solar panels powered by shitty coal plants and basically non-existent when you have build them once and are constructing replacements with solar energy. (The same is true for nuclear btw and also often completely misrepresented in discussion. Nuclear plants in a country full of nuclear plants have a much lower carbon footprint. That's not some technological or scaling effect as often claimed but the simple fact of building the reactor and enriching the fuel with energy already green)

A 100% renewable grid would need a lot of batteries and that too could drive the price up

Actually no. The grid would need batteries (but also alternatives like capacitors or fly-wheels) for short-term stabilisation, but the amount is limited. The grid also need long-term storage but here batteries are completely inadequate. Also the requirements for batteries are usually misrepresented. No, we don't neen some bullshit Lithium-ion batteries or similar stuff requiring rare earths and other rare ressources. Those are used in handhelds where energy density is the main concern. I can perfectly build a stationary grid battery cheaply and without rare ressources as nobody cares if that building-sized installation is 5% bigger and 30% heavier than a build with lithium-ion batteries and also gets 20° hotter in operation... because it's not a handheld.

Case in point: One of the very first things that happened in Germany the moment the new government was sworn in and long before they could actually do anything: energy companies started installing the first battery-based storage units as they now were no longer intentionally sabotaged in creating storage infrastructure for renewables. What did they use? Car battereis. Used ones that were already deposed. Dirt cheap for costs barely above the recycling value. Because the requirements in grid stabilisation and short-term storage are indeed completely different that in cars (again: energy densitiy vs. low price and car batteries with only 60% of their capacity left were completely okay for that job).