For those where it doesnt show on the home screen:
I was having the same issue this morning. The PS5 version wasnt showing anywhere with my MVP edition physical disc and such. But then i went into the PS Store and on the home screen for the PS Store, I saw a 'button' for MLB the Show 22 and clicked on it, to see what it registered as me having, and it came up with the Free PS5 upgrade right there. You just claim that upgrade and itll let you start downloading.
my PS5 version is downloading as we speak (while I play on my Series X)
(Sorry about the xbox icon, i have it on xbox, PS AND switch this year and my Xbox pre-order came first)