A suburb isn’t “associated” with the urban area in its proximity.
Here’s the Merriam-Webster definition for you:
“an outlying part of a city or town; a smaller community adjacent to or within commuting distance of a city”
Alameda is indeed a suburb of SF.
For some, Sacramento is commuting distance.
No it isn’t. Even by that definition Alameda is a suburb of Oakland
By your logic all of the Bay Area would be a suburb of San Jose