Buddy Daddies
This is the most direct modern rec because it also mixes found-family parenting with professional killers trying to maintain a fake domestic life. Buddy Daddies is smaller-scale and more action-comedy, but the childcare chaos and emotional family bonding are very close.
Hinamatsuri
Both combine absurd comedy with surprisingly warm found-family moments between adults and a strange child with special abilities. Hinamatsuri is more deadpan and slice-of-life, but fans of Anya's chaos usually enjoy Hina's equally weird disruption of adult life.
Kaguya-sama: Love is War
The connection is the comedy of overthinking: characters treat normal social situations like tactical warfare. Kaguya-sama is romance-focused instead of spy-family action, but fans who like Spy x Family's exaggerated mind games and reaction humor often enjoy it.
The Way of the Househusband
Both get comedy out of dangerous professionals trying to act normal in domestic settings. The Way of the Househusband is more sketch-based, but the contrast between criminal/spy seriousness and everyday chores is a very similar joke engine.
Barakamon
Barakamon has less action, but it shares Spy x Family's warmth, child-adult comedy, and found-family comfort. Fans who enjoy the softer side of Loid, Yor, and Anya's home life usually like its wholesome village interactions.