Cross-save will apparently be introduced in Genshin Impact version 2.0, according to Genshin Report. Granted, the account does advise you to take the tweets with a grain of salt, but this is nonetheless an interesting development. Currently, the cross-save feature is slated for mobile, PC and Playstation versions of Genshin Impact, namely, all its currently available platforms. The feature will be made available for Nintendo Switch, as well as allowing for Hoyolab, the game’s forums, to be accessible on consoles.
One of the caveats for the feature will mean that platform exclusive items, such as the Descension items on Playstation, will not be available for use on other platforms. Genshin is supposedly also making its way to Xbox, though we likely won’t be able to see that anytime soon when the Switch one isn’t out yet.
UPDATE 9 JULY 2021: Cross-save has been confirmed! Details are available through the official forums here. TW, HK and MO players will be unable to utilize this cross-save function between Playstation and PC / mobile and vice versa, however. You will also be unable to unlink accounts. Genesis Crystals purchased on one platform is unusable on another, so you’ll need to return to your original platform of purchase, nor is cross-platform purchase currently supported.
In the mean time, don’t forget to clear out the Echoing Conches before the Golden Apple Archipelago leaves at the end of version 1.6.