Sinking in your parking spot is a load bearing failure, caused by insufficient subgrade thickness and/or substantial water saturation of the underlying soil. You already suspect this, although “it got washed away” isn’t plausible.
The necessary thickness of base depends on your soil composition - see later in the linked video where he talks about the “force cone” spreading downwards to the native soil. The thicker your base, the larger the area of soil that force applies over and the more durable it is.
But you want actual numbers and you’re a homeowner with a relatively small job talking to possibly shady contractors. I can’t really help you there. Reliable numbers will only come from an engineering firm and they would be doing soil sample analysis. The contractors all just want to do a Good Enough job and they know that homeowners are very sensitive on price so they will ~~skimp~~ economize for you where they think they can.
Everyone should be offering “class II road base” under the asphalt, which is a mix of sizes in crushed stone, all with sharp/angular edges to resist movement.
Not a complete answer but hopefully that gives you a better baseline understanding in future conversations. Good luck!