The Silk of Earth-71490 (Albert Moon Jr.) isn't fully connected to the Web of Life and Destiny, that's why he wasn't recruited to the Spider-Verse fight.
Spider or not, Cindy Moon's Silk is still connected to the Web, she has been in the Spider-Verse wars. However, Albert isn't, and I have proof of it.
Here's the last page of Cooper's story from Edge of Spider-Verse Issue #5:
Now, when Spider-UK (Zarina Zahari) enters Cooper's universe, she only calls for Cooper. She doesn't say "Web-Weaver and Silk of Earth-71490"
Now you may be thinking, but that's because Albert's not wearing his hero suit. Now, you bring up a good point! However, at the end of Charlie's story from Edge of Spider-Verse Issue #4, both Madame Web (Julia Carpenter) AND Spider-UK came to recruit her.
During that time, Charlie ISN'T wearing her spider-suit. This means that Charlie is connected to the Web and that they know her outside of Sun Spider. Another add-on is that Charlie ALSO made an appearance in Spider-Verse Vol 3 Issues #3 and #6 so she has some experience.
So, if Albert is spider-powered and is another version of Silk from a different universe, why isn't he connected in the first place?
I know one thing's for sure, Albert and Cooper WEREN'T bitten by the same spider. If they were, they would've known way ahead.
I still haven't figured out why or anything but my guess is that he's only starting out as Silk and hasn't gotten AS much experience as Web-Weaver. Either way, I hope they somewhat address this.