I don't think any public timeline is available, but statements from all sides make clear (i) Alpine wanted Alonso not Piastri, (ii) Alpine had no contractual claim on Piastri when he chose to leave, and (iii) Piastri had a McLaren contract either signed on in final negotiation prior to Alpine announcing him
They mostly quoted Szafnauer who said a whole bunch of frankly outrageous things both at the time and to camera on DtS. The person whose reputation should have suffered most from this is Szafnauer.
More generally, even if he had free choice, I don't think it was a bad choice for Piastri. McLaren had probably the better car last year, a new wind tunnel coming on line soon, and a lot of promise. Even this year I think they're better than people realise, I suspect in a clean race they're about level with Alpine.