Since saves from version 0.06 not works is it possible to play new events with Gracie without starting new game and replaying all her (and other characters) events from very beginning?
because starting it all from very beginning it's madness...
No.
The game had a massive gameplay overhaul (Wilfred's Contracts) from v0.06.5 to v0.07 (you must have missed that update).
So back then (last year, when v0.07 released) everyone had to start it all from very beginning again.
You may not like it, but everyone was in the same boat as you at one point (whether they started again last year, or starting again now if they missed the v0.07 update).
Even when starting version 0.08 without any saves inside, in "Replay room" I can still replay events I already played before, but there are no new events from latest version.
That's because the gallery for v0.08 content has not been updated yet.
That might come as a small patch later or perhaps even just be postponed to the next update (i.e. season finale update).
Noone knows except for the dev (and perhaps the coder).
But do you really want to experience the game this way?
Sure watching it through gallery you'll likely view all VN part of the game, but all the dialogues, banter and the story which is told through the gameplay (i.e. the Contract gameplay system you missed out on which was introduced in v0.07) that's not included in the gallery at all (and can only be seen through actual proper playthrough).
If you don't care about that part and only VN aspect matters to you, then I guess you might be content to wait for the gallery to be updated by the dev, but otherwise if you wish to see/read the full story, I don't think gallery is really the option I'd recommend.
Maybe there are some unlocker for all events in "Replay room" or something like this,
Given that dev himself didn't update the gallery yet, that's highly unlikely.
Not unless you can find someone with enough coding/game development skills to actually physically update the gallery themselves.