A friend recently asked me for cooperative board game advice, and since we've been very actively gaming through the last seven months of insanity, I thought I'd share some opinions
Codenames Duet
Classic word association game that you and a partner could play and the kids could 'assist' to whatever level they feel like. Best for proficient readers though. Big focus on Theory of Mind and knowing how someone else will interpret the verbal clues you give them. Infinite variety on replay.
My partner's latest obsession, only requires number and color recognition, great trick-taking cooperative mission based game that's fast to play but gets very challenging near the end of the campaign. Awesome for a mixed age or skill group, and replayable.
A favorite role-playing and story-telling game in our household, accessible to any and all. BFF is very open ended and amusing, with just enough structure to keep it moving but super easy to learn. Replayable and lets you record your adventures in a delightful logbook to reminisce.
These 'escape room in a box' games have been fun for me and my partner, and the kids often get involved to help. Easier ones are good for middle-grades kids, harder ones are stumping the adults regularly. Takes about two hours, but can easily be broken up into multiple sittings. Good mind-bending coop puzzle solving, and easily enough clues included to get you unstuck without internet searches.
and one oddball...
Building and economy-making game, competitive but not aggressively at all. I add it because we played the core game it's based on a lot for early math skills, and other families I know have had success with it. A great foundational learning game to understand engine-building and cost/benefit trade-offs, but still approachable by a six-year-old.